Evicting tenant... deposit rent check or no?

[James W.]

I have a set of tenants that were on the fence about continuing lease. 

I decided NOT to extend their lease, and actually did everything right on this one, sending out the proper notices etc - they were supposed to be out by noon on the last day of September.

Now on the 1st of October, one of the two called to beg to renew the lease. Whatever, come in and sign the lease - BOTH of you, and know that this is the LAST chance I am giving you.

She shows up alone, with the rent check. We make it very clear that the other party needs to show up to sign, no later than end of business on Friday.

This one tenant signed, but we did not give her a copy of it as it's not complete without the other party's signature.

Other tenant never showed up, so I feel comfortable going to the courthouse and getting a date and forcing them to leave. 

My question is... do I deposit the "rent" check, even though I am not going to extend their lease? They are still in the residence, with no lease. They received proper notice to vacate.

Or should I send it back with a note stating that they do not have a current lease and in fact should have vacated already?

Obviously I'd like to deposit the check to cover my additional expenses, but my kneejerk thought is that I'm in a catch-22 here.

Give me some hope please! :D

TIA BP