Why would there be “extenuating circumstances”? St. Thomas More, and Catholics of that era generally, didn’t think that this was a bad thing. They didn’t need extenuating circumstances. They would have needed extenuating circumstances not to go after people they thought were heretics.
That being said, the statement is exaggerated. I’m not sure exactly what role More played in specific trials and executions, but as Lord Chancellor he certainly promoted and supported the suppression of heresy.
A notable Catholic patristics scholar once denounced More in my presence (in front of a lot of secular and liberal professors and grad students) as having an “inquisitorial personality.” I stammered out an extremely lame response, because I found this charge off-putting. As a student of the sixteenth century, I take it for granted (perhaps too easily) that the people I study had views about the persecution of heresy that I find repugnant, but that this didn’t mean that they were bad people.

If they actually enjoyed persecuting people or did so out of personal malice, that would be a point against them.

(Some would make this claim about Calvin’s persecutory activities, though I think that’s unnecessarily harsh.) But I see no reason to think that St. Thomas did anything of the sort. He did what he thought was his duty as a Catholic involved in the civil government. He would no doubt have had me arrested and interrogated, and perhaps have had me whipped or made me do some humiliating penance. (I wouldn’t have been burned, since I have no great commitment to Protestant principles.) That would have been unpleasant. But I wouldn’t have taken it personally (assuming that, anachronistically, you could transport me to the 16th century with my opinions and personality intact!).
Edwin