From the internet:
This idiom is used to describe a person who appears gentle, but is determined and inflexible underneath. (‘Iron fist in a velvet glove’ is the full form.)
And a brief excerpt from the article, James White: Slanderer, Spiritual Harlot, Hypocrite:
JW: Before continuing our response to Paul Owen’s velvet-glove treatment of his former religion, …
Parallel: Interestingly, most Calvinists treat their former religion of Arminianism in just the same way. They speak peace to their former selves. They talk about the “process of sanctification” or “growing in grace” going from Arminianism to Calvinism. They do not treat their former Arminianism as idolatry; they do not believe they were bringing forth dead works and fruit unto death. They have not repented of their former religion. This shows them to be just as lost now as they were in their former religion. Paul Owen is just as lost now as he was when he was a Mormon. And Calvinists who believe they remained Arminians for a time after they were regenerated are just as lost now as when they were Arminians.