If they do not pass the credit/criminal background they will be denied. 

I called hgim to speak about it verbally and when I did he became aggressive with me on the phone and denied any wrong doing.

I'm pretty sure it violates Fair Housing Law to deny an applicant based solely on whether or not they have tattoos.  

How would I respond, I would deny them.

3) They require that the owner or designated property manager be available and can be contacted 24 hrs per day, 7 days per week regarding the rental unit4) They can deny issuance of or revoke your registration application so that you cannot rent your property5) The fee for one unit starts at $100 per unit per year and can go up to $2000 per unit if you ever have code citations...please see the fee schedule.....Click Here to see the ordinance and resolution These type of regulations have a way of "growing".

Trying to understand the likelihood of being denied all together.

Or now you want to rent that unit and deny every woman qualified or not , waiting for a male tenant , you just got for a discrimination lawsuit . 

William,All FHA, VA, and USDA loans are qualifying assumable and a bank can't deny an assumption of these products. 

I understand we can't do more than 80% LTV in Texas but I apparently misunderstood how this works as I was denied today BEFORE an appraisal was even ordered.

If they get denied I will just set up a rent repayment plan for the past-due rent.