I saw this sentence in a TV show
The sentence should mean there is nothing to talk about. But why are there two てs in this sentence?
Why can't they just say:
First, 立つ is intransitive and 立てる is transitive, although they are both "to stand" in English. The te-form of 立つ is 立って, and the te-form of 立てる is 立てて. The first て of 立てて is part of the verb stem, and the second て is for making the te-form. Two て's can appear in succession in the te-forms of タ行 vowel-stem verbs such as 捨てる, 当てる, もてる.
As a compound verb, there is no such word as 取り立つ at least in modern Japanese. But there is a transitive compound verb 取り立てる, which roughly means "to pick up something/someone as a special one." 取り立てて is the te-form of 取り立てる. (取り立てる also means "to collect tax/debts," but this meaning is not relevant for now.)
One of the functions of te-form is to make certain verbs adverb-like. See: What is the role of あるいて?
So a rather literal translation of 取り立てて would be "in a manner of picking up / focusing on something". Practically, you should remember this as an established word that just means "especially", "in particular", etc.
取り立つ話題がない is wrong because 取り立つ does not exist in the first place.