This is just an idea, but what about having guardian creature attached to a beacon. This creature will roam around the players’ beacon area and remove any blocks placed in the immediate vicinity placed by players without building permission.
Also, you could add features like being able to train it (black and white style) or evolve it, or something.
having a pet for this purpose would be complicated to program. do handle the griefer problem with regeneration processes seems to be easier to make and also effective (may be the regeneration process can be speeded up near your beacon to clean stuff for example).
For the matter of pets and the possibilities with them just have a look at other topics (just search for “pets”. You will find many of them 
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While it sounds good in theory, you only have say over what is inside of your Beacon. You can’t control what others can build outside of it.
yepp, just would be a way to speed up the regenrration if the area is not occupied by another beacon. And for that there are many easier ways to handle it
I had the idea of griefer animals like little monkeys who sometimes come and snatch away your crops or mined material. Your idea could just be the opposite of my idea. Helper guardians or creatures.