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Solving the simple cryptic clues gives the following answers:
Each answer has double letters in it, and if we join them all together into a single string we get even more doubled letters: AMMOORRERYPEERREEKADD. If we remove the doubled letters, we get AERYPKA — the extra string provided as part of the puzzle; this clearly means we are on the right track. The idea of removing doubled letters also explains the title of the puzzle, "Pule", which we now realise is "Puzzle" with the double letter removed.
Since the single letters were provided in the puzzle, it makes sense to look instead at the doubled letters which were removed. Looking at each pair as one letter reveals the message MORE RED. This is a thoroughly un-cryptic clue to REDDER, which has the interesting property that if you recursively remove doubled letters you eliminate the whole word.
The solution is REDDER.
This puzzle was inspired by a sign (in Japan, though written in English) on which two adjacent letters had faded, which happened to be the same letter. It made me imagine that they'd somehow cancelled each other out, like some kind of self-inverse elements.
We made a version of this puzzle with additional graphics which more strongly captured the theme of doubled letters eliminating and thereby made the answer more compelling, but eventually decided that it provided so much opportunity for distraction that it made the puzzle harder rather than better. One discovery in this process was that it's basically impossible to graphically represent the concept of "nothing" in a diagram for a puzzle (which was used to indicate the self-eliminating property of "redder"), as distinct from an empty space which we want the solver to fill.
Another interesting fact: There are very few even length palindromes that are common words. At one point I was concerned about using "redder" when it was almost the only word that could be the answer, but certainly in this presentation by the time that becomes clear the puzzle is solved already (though the hints in combination do change that).