テレビ「は」あまり見ませんが [...] As for television, [I] don't often see(=watch) [it] but [...] (~ I don't watch television much, but [...]) テレビ「を」あまり見ませんが Television [I] don't often see but [...] (I don't see *a* television much, but [...]) In the first sentence, the topic is (は, "as for X") TV. What comes after it is "don't see often" which is equivalent to "don't watch much" in this case. In the second sentence, the implied topic is television, but を implies you directly use it to perform/act out/do the verb after it, in this case seeing. 〇 テレビはあまり見ませんが、嫌いじゃありません。

テレビはあまり見ませんが、嫌いじゃありません。