What would you do? Potential renter with a felony.

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We put our home on Zillow/FB Marketplace/Avail about 10 days ago. I've gotten a lot of interest, but no follow through. A potential renter wanted to see the house but asked to fill out the application first. I thought that was odd, I offered that she see if first or call with any questions. She called and told me straight off that her husband has 2 prior felonies. First was in 1994 and the second was in 2014 and he is on probation. Am I naive to consider them? I'm considering giving them a tour just to see how I feel when I meet him. She also told me they had a home-fire and are staying in a hotel and want to move in asap. Is that another red flag?