Sorry, but I’m with SD_R on this one. There is legal and then there is right. One of the reasons we are all going to be having problems going forward is because of people who are taking advantage of the weaknesses in the system. Finding and exploiting a loophole at someone else’s expense isn’t right regardless of how it’s done.
You’ve offered your rent receipts to the lender, which I think is commendable in itself. They haven’t responded so far, probably because they have no right to those rents until they take the property back. No response isn’t the same thing as refusal. If after they foreclose they still decline the accrued rents to offset their other losses then I’d say that on an ethical basis you’re in the clear to keep them. Other than that…..