Je pense que dans cette expression « la » se réfère à la situation.

Faire un tel faux pas au premier rendez-vous ça fiche mal la situation.

Please put your vulgarity googles on, we’re walking into the wastelands here.

“ça la fiche mal” is the tame way of saying “ça la fout mal”.

“fout” is the verb “foutre” which basically means the old in-and-out. Like screwing, but not the kind that involves a bolt. It also means ejaculate.

“Fiche” when used as a noun is an electrical socket or plug. But you anglos also have “mating” connectors, so we’re even. The verb “ficher” has several different meanings but the one we’re concerned about here is “to thrust into, to stick in.” You could use it with an arrow, if you’re into that sort of thing.

The meaning of “la” in “ça la fout mal” can come from two different sources:

1) “foutre” implies a hypothetical female as jcm69 said.

2) While the French penis is masculine (un pénis) the French slang term for dick is actually a feminine word! (look it up, it’s a girl). I believe “la” refers to it. So it means you stuck it in wrong. A bit like when you say “f- me sideways!”

Such a lovely and tastefully graphic expression!

Now, no-one would ever use “ça la fiche mal”. Either you’re going full crass and you say “ça la fout mal” or you opt for politeness and use something completely different.

“faire un tel faux pas au premier rendez-vous, ça la fiche mal.” is a bit ridiculous in this regard. “Faire un tel faux pas” is extremely formal. If you want to go full crass, be my guest, but don’t mix crass and formal in the same sentence…