As a general rule teeth whitening strips are not bad for the teeth, with simple ones causing no problem at all. Your teeth could turn bluish permanently if used more than what is directed, with the teeth turning brittle. Also most whitening products contain around 3% bleach that is not recommended by health experts, with about 0.1% bleach found acceptable.
It is also to be realized that whitening strips provide for a strip on the upper teeth and one for the lower teeth, each of them pressed against the outer surface. However recesses and grooves between teeth could show up as dingy cracks, more like a painted fence that looks good from outside, but whose groves show up dark and dingy.