"The waiter brings the menu."
Translation:Kelner przynosi menu.
It sounds kinda... fancy and/or archaic, but there's no way to reject it. Added.
For example the word "jadło" for "food" really sounds like (late) medieval ages.
Usually "jadłospis" would be a list of what's being served at what day/time at a school, university etc.
Here's what Google shows me if I want to see a "jadłospis" (from a preschool): http://przedszkoleursus.pl/wp-content/uploads/2014/10/Jad%C5%82ospis.jpg :)
While the first "ta" might have been OK if you really wanted to specify that THIS particular waiter brings the menu and not just SOME waiter, we wouldn't really use the second "to" in this case, at least not in the context of this English sentence.
The only way the sentence you've mentioned would make perfect sense would be if you're writing a review about some restaurant that has multiple menus and you want to talk about how they organize themselves saying something like: "Despite the great variety of meals, the restaurant can handle the staff perfectly - while this waitress brings that menu, the other waitresses bring the second menu"... something like this, to specify that this person brings this menu. I hope you know what I mean :)
Generally I agree, but technically almost every such "the" can be translated as if it was "this", unless "this X" just doesn't make any sense at all in any context. So while it's weird and unadvisable, it's not a wrong translation. Added.
Actually "to menu" worked anyway, "kelnerka" didn't, but in contemporary English it's more and more likely to use "waiter" for a waitress.