Let me be perfectly clear: I'm not saying there was tampering that took place, I am just playing devil's advocate for the sake of answering your question.
Bennett said that he told his agent to inform teams not to claim him. His intention was to get surgery and sit out the remainder of the season.
Alleged tampering would go like this:
Belichick: "Okay, look: we really want you back, but you're too good, there's no way you drop all the way to our spot in the waiver claim. Someone will claim you, if for no other reason to block us."
Agent: "Okay, how about this: we'll let teams know that Bennett plans to get surgery and call it a season/career. That way, they won't even bother putting in a claim on him. This will ensure that he drops to you guys."
Belichick: "Wouldn't that be too obvious though? If you tell the league not to claim him, why would we bother doing it in the first place?"
Agent: "We'll just say you did it because it was 'worth a shot' to try to talk him out of it. What did you have to lose? Besides, I have a feeling that after you claim Marty, he'll have a change of heart about retiring. Wink-wink, nudge-nudge."
Again, I'm not claiming this is what happened. I'm just saying this is what alleged tampering could've looked like.