Tosefta for Chagigah 34:9

We do not bring a thanksgiving offering on the Festival of Matzah (i.e., Passover), because of the chametz that is in it (see Lev. 7:13), nor on Shavuot because it is a Day of Slaughter ("יום טבוח", cf. Tos. Chagigah 2:7, Chag. 17b:2-6; alt. "יום טוב" ("[it is a] Yom Tov"), see Beitzah 19b:2 and GR"A here), but it is brought on the Festival of Sukkot, and one fulfills his obligation [of bringing a Festival offering] with it. Rabbi Shimon says, we do not bring a thanksgiving offering on the Festival of Sukkot, because everything that is brought on the Festival of Matzah [also] is brought on the Festival of Shavuot and the Festival of Sukkot. [Thus] a thanksgiving offering, which is not brought on the Festival of Matzah is not brought either on the Festival of Shavuot or on the Festival of Sukkot. Rabbi Elazar son of Rabbi Shimon says, a thanksgiving offering is brought on the Festival of Sukkot, and one fulfills his obligation of rejoicing with it, but does not fulfill his obligations of [bringing a] Festival offering with it.