I just talked to a lawyer recently about this, First off I don’t think the FBI does any investigating because who ever handles immigration are the ones doing the background check. Also, in your 25 years of being a permanent resident, had you committed a crime that was serious enough they would have deported you for it by now. So besides a standard criminal background check they might look to make sure you paid your taxes. And last, having naughty pictures on the internet isn’t a crime anyways so if they did do a google search I wouldn’t worry too much :P But I am not a lawyer or anything