you will need to have a set of criteria you apply to all applicanants, for example (and just a number here) credit score above xyx, job held for over 2 years, 3 references, employment verification etc, income at least 3xrent  what is your criteria for your area and the value of the house you are trying to protect.Let them mow the grass, but if this is a nice home in a nice class B or class A you might want to service the lawn and put down weed preventer, etc when appropriate. 

I have excellent credit score, but I’m not sure if I can refinance my mortgage for better rate.

They will go up to 80% CLTV with a minimum credit score of 680.https://www.quorumfcu.org/lend...Best of Luck!

Funny enough, I am making more money than I ever had but I am barely lendable due to Credit Score impacted by purchases & my high DTI. 

He has a score around  740, and we are bringing 20% down.

Our goal is to rent your vacant property as efficiently as possible, which requires us to balance how long a property is vacant, rent amount and tenant quality.Screening ApplicantsPoor screening often results in lost rents, legal & court costs and costly damages.Screening of applicants includes the following:Full credit/eviction/criminal checks are done, instead of score-driven reportsVerification of rental history includes validation of actual property owner to avoid fraudVerification of stability of income & employment via YTD paystubs & W-2(s) (analyzed to confirm not fakes)Income is calculated 3 ways to spot stability anomalies: pay period, YTD average and YTD + W-2 average.Debt-to-income analysis (more accurate than traditional 3x rent requirement)Bank statement to see if NSF issues, if deposits support income, prove MoveIn Funds, also analyzed for unusual transactions.Pet screeningHolding Fee required from approved applicants to make sure they are serious, before your property is marked pending.

I was wandering how my credit score will be affected applying repeatedly for mortgages and refinancing other loans on Brrr properties.

With my original screening criteria I would require a tenant to possess a 600+ credit score, 33% rent to income ratio, and a relatively clear background check. 

Get your credit score to the highest possible. 

Speak with your lender or multiple lenders to see how you can raise your credit score, pay off as much unnecessary debt as you can (credit cards, car loans, etc.).