Danger!
If you accept December's rent as paid you might lose your right to evict.
To preserve your right to evict you might have to return the check with notice that partial payment (rent without late charge) is not accepted and they are still in default for December.
Note the word "might" in those two sentences. I don't have the time to scour the statutes to make sure of that but it's been my own experience here in AZ when I had rentals. Make sure of your position before you go through the expense of filing in court.
As tempting as it is to pocket that money, it could get your eviction dismissed and you'll have to start all over again in February if they are late again.
I guess the upside to that is that you have December and January's rent and you might just have to eat the smaller amount of late charges rather than lose December's rent altogether.

