絡む's original usage is like below.
「つたが木に絡む。」: A vine wraps around a tree, and it is hard to take it away.
「ひもが絡む」: A thread tangles.
So, the original verb itself means slightly different. Something long and slim is going around and it is hard to remove or resolve.
There are some derived usages, 金が絡む事件 or 酔っぱらいが絡む.
金が絡む事件: An incident related to money.
酔っぱらいが他人に絡む: A drunken guy is hassling others.
In the former one, money is related to the incident, but in a way like a vine wrapping up a tree and is hard to remove. In the latter, a drunken guy is saying reasons and developing a connection with others like a vine.
Let's get back to the original phrase. 女絡みの is often translated as "something related to a woman/women" but these "a woman" and "related" have a little different nuance.
First of all, 女 means "a woman", but in this case it has sexual overtones. This is difficult to explain, but 女 is a word without politeness. For example,
20代の女性が殺された事件で、警察は逃げた60代の女の行方を追っています。: Relating to an incident that a woman in her 20's was killed, the police is looking for a woman in 60's who escaped. (A common phrase in news programs. They change 女性 and 女 to indicate that the woman is suspected.)
女 is an expression without politeness, and an abstract idea of an attribute. The reason to refer to something that way sometimes indicates sexual overtones. (You may also say 男絡み.)
So, there is an expression like,
彼には女がいる: He has an intimate woman (which suggests it is extramarital). (The direct translation is "There is a woman for him.", but this phrase suggests dirtier relationship. You may also say 男がいる.)
Next is 絡む. It is basically like a vine. So, 女 is deeply related to every part, and it is hard to understand its structure. It is not possible to get rid of it even though 女 makes the situation worse, confusing and complex.
This is basically means "He quitted related to a woman." But, this translation is not precise because of what I've explained above. It is not a certain woman but more abstract woman-related-thing which deeply entangled to the situation and was not easy to fix. So, I expect a complex trouble occurred.