If part of the qualifying spend has been refunded, will I lose the sign up bonus that was given to me?

In my sign up period (with Amex) I booked several flights to get me up to my threshold for bonus points. Got the bonus points no problem. But now 2 flights ($600) are cancelled due to Covid and the money refunded. Will Amex take away the bonus points as technically I now didn’t make the threshold?

They won’t take them away from you. If they’re in your ff account, they’re yours.