Reputation management works, but not in the way some agency websites suggest. It does not delete the past. It does not give you a button labelled "remove from Google." What it does, when done properly, is move the centre of gravity of what people find when they search for you - from a cluster of unflattering or unfair results to a wider, more accurate picture that reflects who you are now.
The honest distinction is between two things that often get blurred in marketing copy: removal (the negative content goes away entirely) and suppression (the negative content still exists but is no longer the first thing anyone sees). Both work in the right circumstances. Neither is universal. The trick is understanding which is realistic for your situation, and avoiding the providers who pretend the line does not exist.