If we look at the meanings, we will notice that the prefix re- means "to do again." The prefix un- means either "not" or "the opposite of". There are a couple of oddballs in this sort, which are words that begin with un or re, but do not retain the meanings of those prefixes.
Here is how the words should be sorted this week:
re- un oddball
rebuild unable uncle
recopy unbeaten reptile
recycle unwrap
refill unselfish
refinish unbutton
remodel unkind
retrace unpack
retake unfair
return uneven
review unequal
rewrite unhappy