So what happens when you do have duplicate people?

True duplicated Persons will appear on the People Index list more than once, or show up twice in the Ancestry List of all People.  If you do not see multiple entries, then they are not duplicates. 

If you recognize two different entries are actually the same person, then use the People > Person > “Merge Two Specific Individuals” command. Verify that you have the correct pair of persons and confirm what data to keep as a result of the merge.   BTW, merging two people will appear as a deletion of one during your next sync.  (i.e. 2 into1 = 1)

Find Duplicate People Tool.
The Find Duplicate People Tool, simply attempts to compare people in your tree with others that MAY be the same person. Each line in the display is ONLY A POSSIBLE MATCH. The higher number in the right-hand column, the closer the computer thinks the match is.  Research each pair before accepting the match and always verify the data being merged.  Note: a single person may be proposed as matching on several different lines.  That's the program just being thorough.

The Goal is not to clear the tool. It is not necessary to clear all the lines on the list. Not finding true duplicates is a good thing, there should be none. Merge those that are duplicates, review those that you are unsure of, and ignore those that are obviously wrong.  Then move on.  Spend your time on research and checking to make sure you don't already have the person in your tree as you work, thereby preventing duplicates at in the first place.
You can remove lines from the tool's list as you work and save the state of the tool so that you can reopen it to continue your review.  But there is no way to permanently remove potential matches.  Each time you run the program anew, it reviews all your data to pickup any new persons and will display many, if not most, of the same potential matches.  

[Yes, I know many people think the tool could be better implemented, but it is what we have, use it or not as you see fit]  Many find reviewing the Index to be more productive.