Question on Filing for Nonpayment

[Wade Garrett]

Let's say I have filed for eviction today, Jan 11, for rent that was due January 1. And in the time that the complaint is processed and we are granted a court date, the tenant sends me a check for the rent. 

If I want to evict this tenant, I am not supposed to cash the check so as not to disrupt the eviction process, correct? But then I am conceding to not being paid from Jan 1 until the day the tenant moves out, even when they have offered to pay (late). 

The whole point of eviction laws are so that landlords don't get screwed out of money. Do I ever get January rent after the eviction takes place? What am I missing?