The article is needed in the course to help you remember the gender of words, it doesn't mean that we always use it. In this case Τρίτη is a perfectly normal response to the question "what day is it today?" (τι μέρα είναι σήμερα;) - and it would be wrong to use an article.
It's a bit confusing for me. In my language, we also use numbers for the week days but we start with Monday, so Monday = 1day, Tuesday = 2day, Wednesday = 3day etc. In Greek I always have to add +1 in my head :D
I noticed that the Greek words for "Monday" and "Tuesday" correspond to the names of the chemical substances "deuterium" and "tritium" that are only distinguished from each other by the different numbers of protons, that is 2 respectively 3. Greek is really cool!