depends what you want

if you want to continue your eviction case after notice and filing at court, you can just keep this check till clerk finally makes judgement, and after that you can deposit that check whatever..

If you want to give up your case, then cashier check or money order is acceptable. Personal check is just a tricky game and don't take that now..even don't try it..

If you own the same bank as that check, for e.g..that check is from bank of America, then you have account at bank of American, you can try to check if your tenant has enough money... in case bounced, the same bank won't charge you penalty fee normally. But different bank with transferred fee, then would charge you bounced fee.