I don't think it would be worth their trouble to bother. New coop members would be able to scroll down thru the chat bar to see the gift messages so blocking them somehow would be a nuisance. Besides, there us still the 10 gift limit total so it's not like there is a huge opportunity for abuse in the middle of a regatta race. Right now, it would only really help for players who don't race.
If they were that concerned you would think they would set the gifts to expire the same time as the current race. Ours show and extra day plus.