イチャモン (いちゃもん, ichamon) is a casual but advanced Japanese word meaning unreasonable and/or nitpicky complaints. It is usually used as “イチャモンをつける”, meaning ” to give unreasonable complaints” or “to nitpick”.
“イチャモンをつける” and “ケチをつける” are synonyms to each other, and these expressions are basically interchangeable. The slight difference would be: ケチをつける is more often used when someone complains about something that is great enough and satisfactory for a majority of people. For example, ケチをつける is more suitable to use when someone complains about the performance of an MVP player. Another difference is that “イチャモン” can be used as a noun by itself meaning “complainant”, while “ケチ” cannot be; interestingly, “ケチ” is usually used as a na-adjective that means “stingy”, which is considered to be irrelevant to the idiom (although these words seem to share the same origin).
Most of the criticisms are イチャモン (unreasonable complaints), so you needn’t worry about it.
You should keep away from people who always イチャモンをつける （make non-sense complaints）
Don’t ケチをつける (make unreasonable complaints/negative comments) about others’ lifestyle
Synonyms: 文句 (complaint), 言いがかり, 難癖
Synonyms in English: nitpick, complain
Related words and phrases: ケチをつける