I was a little confused by this at first, but I think I've finally twigged. I take it that your variant is American English, so you don't use "on" talking about a specific day, "We're meeting Thursday". But in British English, we use "on" in both contexts, "We're meeting on Thursday".
So if I'm right, when you talk about the use of "on", the fact that we're talking generically, "on Thursdays" is taken for granted. I'm afraid this wouldn't have been so apparent to British speakers.
I'm not American and I wasn't advocating that "the Thursday" made sense in English. I was explaining that that is the literal translation from Romanian, that in Romance languages the way they say this is "the Thursday", whereas in English it's "on Thursday" except for certain Americans.
If, as has been suggested, this use of the defininite article follows the standard Romance language pattern, for example, "il giovedi", "le jeudi", it means "on Thursdays", rather than what I'd normally understand by "on Thursday" (i.e. this Thursday. at least in BrE)
And this indeed seems to be the case:
We often go to the movies on Thursdays.
- "De obicei mergem la film joia."
We'll continue this discussion Thursday.
- O să continuăm discuția joi."
It appears that the translation here, if not perhaps incorrect, is at the least misleading.