We have bought all of our properties via the MLS, we make offers that will cash flow which means that many of our offers are rejected.

However, it is also important to consider the applicant's income level, employment stability, and any other positive attributes they may bring to the table.Ultimately, the decision to accept or reject the couple as tenants will depend on the landlord's specific policies and risk tolerance.

The need to screen tenants is critical, but with mid term tenants it is often (as often as monthly).We just rejected a 90 day rental on one of our STR units.  

We often find opportunities to make Conventional work, which means a rate that's likely 1% less, no prepayment penalty period (most but not all programs have such), less risk of the deal falling out due to a low rent estimate from the appraiser, and less chances of your offer getting rejected due to it being "other" type financing.

The more deals you analyze the better you will be at it and the more likely you will be able to find a good deal.Most deals don't work, we look at more than 100 deals and reject them for every one we try to do.

If I wanted to get it terminated earlier I'll need to get an appraisal (paid out of pocket) and have it sent in for their review upon which they still could reject the removal. 

Could an applicant claim that you rejected them based on protected status?

You can use a Quit Claim Deed and that can be rejected when you go to sell the property.11.

They can't counter or reject at this point, right?

I operate on the more you tell a rejected applicant the more they can use against you but once you say you have collected move in funds from another tenant it is pretty much over and if not I just ghost.