I don’t think the overwhelming majority of LIBRARIES are out to steal your music. If they remove your tracks and you can verify they’ve been removed, it’s extremely unlikely they will re-title them to sell them illegally.
Thefts are more likely to occur from individuals, not businesses that want to stay in business. (Nothing’s impossible, of course).
The bigger concern is being sure that they actually remove the tracks and they are not floating around on media out there, still being considered for opportunities, while you sign an exclusive with another library.
Basically, I wouldn’t worry about it. If you ask for removal and they appear to have been removed, all is probably fine. You might want to wait a while before signing an exclusive, making sure all the dust has settled.