discovering workman is a convicted felon-what are landlords obligations?

[J.N. Miller]

I ran a criminal check on a workman  recently hired & found out he is a convicted felon & was in prison until 2011 ( crime-identity theft). Our ad specifically said do not apply if you  cannot pass a criminal background check.   He is a good worker, but I am very concerned about having him work on occupied properties (so far I have only had him do exterior yard work on vacant houses)--   When I confronted him  about what we found, he said that I was happy with his work so why am I concerned about lhis past & doesn't everyone deserve a chance, etc.

What would other landlords do?