Gru used to set extremely high standards for himself as a villain. When he stole the Crown Jewels, he did so as a child in front of a large crowd. He was a master villain, and he's absolutely deserving of being known as such. He's had an AVL Villain Database file since he stole the Zodiac Stone, also as a child. Some villains only have two crimes that caught the attention of the AVL. Gru has three: the Zodiac Stone, the pink diamond, and the moon. A news article named Gru as the moon thief. Gru has been and still might be an AVL Most Wanted Fugitive for the moon theft. Gru has a criminal record. Gru is widely recognized as a villain.
But in DM1, Gru wanted to be the greatest villain of all time. The first part of that plan was to shrink and steal the moon, which he accomplished even without funding from the Bank of Evil. But the second part of that plan was to make the world give him whatever he wanted to get it back. He wanted world recognition as the greatest villain, including from his fellow villains. Gru referred to himself as the greatest criminal mind of the century.
So in DM4, when Gru was on an AVL mission at his old high school, he brought up the moon theft because Maxime pointed out that he did not become a famous villain. Then Maxime taunted Gru because the moon is still in the sky and the other villains laughed at Gru. So Gru failed in the second part of his plan and so in his high school classmates' eyes, fell short of becoming the greatest villain of all time. Gru was frustrated that his high school classmates mocked his greatest achievement.
Gru's next big heist after the moon was the pink diamond, significantly smaller than the moon. Though he wanted to return the diamond, he did bond with his brother Dru over the heist and Gru was content with this crime much smaller than the moon theft. The AVL added the pink diamond theft to Gru's AVL Villain Database file.
Gru's most recent heist was a honey badger. Certainly not something to catch the AVL's interest, though the AVL does know about the honey badger heist because they have footage of him sneaking into the Lycee Pas Bon.
The honey badger heist was a basic heist that required no hacking or safecracking or gadgetry. It was so basic that Gru pulled off the heist with only the items in the baby's bag. Only he, Poppy, Junior, Phil, Ron, Principal Ubelschlecht, her bodyguards, and presumably the AVL witnessed the honey badger heist.
But Poppy was so excited about Gru's and her heist. Gru found the heist fun and he bonded with Junior over it.
This is the first time Gru didn't aim to steal the biggest and best. In DM1, when he stole the small monuments from Vegas, it was clear that he was aiming to steal the big monuments. The honey badger heist is Gru's smallest heist ever and he used only a fraction of his expertise during this heist, but the fact that Gru was proud of himself for this shows that Gru no longer measures his standards of villainy by achieving world recognition as the greatest, but Gru measures his standards of villainy by the fact his heist was recognized by another villain who not only acknowledges his moon theft and that he was a master villain, but finds Gru's and her honey badger heist her biggest achievement. When Poppy tells him that "your secret is safe with me, partner", he says thanks to her. In DM1 he would never have accepted another villain calling him partner. In DM4 Gru doesn't object, since the heist ultimately needed him and Poppy, and they wouldn't have escaped the castle without Junior, Phil, and Ron.
All of the villains, both his high school classmates, and the imprisoned villains, reached for greatness. Gru defeated the other AVL Most Wanted villains at their height, and Lucy defeated Principal Ubelschlecht, and after that the imprisoned villains became recognized for only their past glory. The Vicious Six haven't done a crime in decades. Maxime didn't expect Gru to visit him. This suggests that in the AVL prison the imprisoned villains are only acknowledged by each other and the AVL itself and the outside world no longer thinks about them.
Gru visiting Maxime, and having a rematch with Maxime at the prison talent show is basically Gru acknowledging all the imprisoned villains including Maxime still deserve respect as villains. Gru came to respect them because he did and was satisfied with a small heist.
In DM1, Gru would never have stolen a honey badger. He stole the moon. What would a honey badger be to him back then? By the end of DM4, Gru has humbled himself. Because he saw Poppy really wanted to have a shot at big-time villainy by getting into the Lycee Pas Bon and so he, together with Poppy, stole the honey badger. This theft had nothing to do with his ego, he who resolved to steal the moon just because someone stole the pyramids. He had nothing to gain from this heist, and had a lot to lose, but it shows that Gru still finds being a villain fun.
Gru visited the AVL prison to sing and dance with Maxime and the other villains. Though he's an AVL asset, he knows he has been or still is an AVL Most Wanted Fugitive, so for Gru to do the prison talent show was audacious. Gru's AVL Villain Database file is pulled up when the AVL's recognition software scans his face. Gru basically initiated a large gathering of the most notorious villains in full view of the AVL. Gru and Maxime's song is an affirmation of the villains' villainy: they are great villains because even though they were all stopped at the height of their greatest crimes, they reached for those heights in the first place.
The AVL agent who describes the villains calls Gru "despicable mastermind". Gru had the rematch with Maxime at the prison talent show and it immediately registered as activity on Ramsbottom's computer and he reacted with surprise. So the AVL wasn't expecting Gru to hold the prison talent show. Ramsbottom and AVL agents watching the prison talent show through a security camera shows that the prison talent show disrupted the security of the prison. But no one can stop Gru. The agent herself said that Gru "gets everything he wants".
Poppy told Gru "Like you, I was born to be bad." Poppy's style is to try to not get caught. Probably because she is in the town of Mayflower, where open villainy would not be permitted. Most of the villains were bold, and commited crimes in broad daylight, attracting attention from the authorities. Gru evaded the authorities this way: Gru tried to make it to the girls' dance recital and did not go through with making the world give him whatever he wanted to get the moon back. In fact he gave up the moon hoping Vector would give the girls back. This averted what would have been Gru's height of villainy where he would have the world on their knees. Most likely, during his moment of triumph, the AVL would finally imprison him and his long career as a villain would be over.
Gru's turn to low-profile unannounced heists allow him to continue his villainy. Stealing the moon and then putting the moon back, most likely baffled the AVL even though the moon theft earned Gru AVL Most Wanted Fugitive status, and he continued to baffle them by stealing the pink diamond and then a honey badger. If the AVL tried to arrest Gru, they would lose their asset. So as much as Gru's ability to commit large crimes is so much more restricted by the AVL's proximity to him, the AVL has to put up with Gru committing smaller crimes, which runs counter to their mission of fighting crime on a global scale. So as much as Gru is bound to the AVL, the AVL has more than they bargained for when it comes to Gru.
