When the police or prosecuting authorities "drop a case", they withdraw a prosecution that they started, perhaps because they could not obtain sufficient evidence. The reason doesn't really matter - it's the action of withdrawing the case. "to screen someone" in this context is to vet or check them out before they are authorised to do something. So here, match.com will not allow their clients - people who want to date others - to use their website until match.com have checked that they are not sex offenders. Another common use of "screen" is call screening. On many phones, you can see who is calling before deciding to take the call. This process is "screening" - a gerund.