Why do Catholics kiss their thumb after making the sign of the cross?

The reason they kiss their thumb is that they’re making the sign of the cross with their forefinger finger and their thumb. So, they technically aren’t kissing their finger, but kissing the Cross they make with their fingers. This is not a bad practice since it is a sign of reverence to the Cross of Christ. It is just like how we learned to kiss the Cross on our Rosaries before praying the Chaplet.

The practice of kissing the Cross is an ancient custom showing a person’s devotion to Christ and also acceptance of one’s own life’s burdens. If done presentness of mind and reverence, I am sure this could be a source of blessing and grace.