Answer: I would contend that the right answer is "more gentlemanly."
Explanation: Just to elaborate a little on the answer, it can be added that when forming a comparative adjective—as the one that the example requires, since it is followed by "than"—it is necessary to take into account the number of syllables of that adjective. If it has three or more syllables, as gentlemanly, the comparative is formed by putting "more" in front of the adjective.
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