Mooney M20 pilot reported losing control of the aircraft while attempting to land in gusty crosswind conditions; resulting in the propeller striking the ground.

Narrative

I was landing at ZZZ with three passengers on board. Winds were a gusty crosswind; as forecasted. They were 190 at 15G26 and I was landing on Runway XX. That crosswind was within the plane's capabilities and my experience. Over the runway; I ballooned. As I tried to get back on the runway; I bounced. As I came back down and tried to recover from the bounce; my right hand unintentionally advanced the throttle a bit. I pulled the throttle to idle and completed the landing. After shutting the plane down; I saw that I had suffered a prop strike on landing. I feel that I obviously need to work on my landing technique; especially in crosswinds. I also should have initiated a go-around after the bounce as opposed to trying to salvage the landing. Contributing to the incident was the fact that I was doing a public-benefit flight for a couple and their little girl; and I very much wanted to get them home quickly. That led me to be less willing to go around. I had picked out an alternative nearby airport with a runway better aligned with the winds; but I think that my desire to get this family home as conveniently as possible led me to reject the idea of landing at my alternate.