You can certainly remove a profile if you don't want them to reappear in your search results. You can do this by clicking 'Don’t show again' under the small down arrow at the top of the profile.This helps you to refine your search results.
If you wish to reconsider them later, you can access these profiles from "Matches" Tab >> "Recently Viewed" >> "Ignored Members".
P.S. This is currently not available for our iOS App users.