This sounds ridiculous, which must mean it's USA. You pay the check into the landlord's account directly, or you can do the same with cash. You do a direct deposit. You get written evidence (email) that the landlord only wants a check in an envelope to a certain address. If you have certified postage the onus is on the landlord to prove the envelope was empty. After all they could have given you a bank account number or a way to give cash in hand.

I seriously doubt you can evict tenants if the only argument is that it's uncertain whether the envelope was empty or not.