He apparently had Queens about as wired as anyone could have an area. Had cops on payroll, friends in the courthouse, tipsters and debtors in dozens of local businesses, the biggest warehouses of any major hijacker. He was quite the asset available to all families as well as an inviting host to amateur criminals and made crime in Queens run vary efficiently for a long time, considering.

He also managed many of what could be considered Vario's "young turk" faction. While members of the Vario Crew like Bruno Facciolo and Steve DePasquale were direct with Paul for certain rackets, between Hill, Tommy D, Angelo Sepe, etc.. Pauly seemed to be ultimately less direct with all of these men although they belonged to him than Burke was. Pauly seemed completely direct with few people from what I've read and Burke was on of them who by extension spoke and listened to Pauly for several lower tier members.

I think this added as well, as @alfa_romeo stated, to the difficulty to actually even attempt to kill Burke. He socially surrounded himself with somewhat rouge soldiers many of whom weren't made or even !00% Italian and killed at will and and blindly followed Jimmy. It would have been risky to attempt to say the least and you have to consider during the timeframe who would even dare take on the contract?

Not to mention as I stated in my above post, I think realistically the Gambino Family was more than satisfied killing Tommy DeSimone for the Batts and Fox Jerothe murders and having Tommy Agro kill him and not really keeping that much of a secret was clearly the message to be taken as retaliation for Batts. Too many Gambino men earned with Burke to honestly have cared. You have to safely assume the loansharking/bookmaking operation in question that Burke took from Batts profited more with Burke operating it at his height as a criminal than it did with Batts operating it before he went to jail. Given that, whatever Gambino tribute that needed paying would have been a regularly larger tribute from Burke so, that kind of answers the question.