TT #59 · Parashas Reeh · First Aliyah · Passuk 12:15
However, in all the desire of your soul you may slaughter and eat meat according to the blessing of Hashem your God that He has given you in all your gates; the unclean and the clean may eat it, as of the gazelle and as of the deer.
Torah Temimah points to Sifrei / Bekhorot.
English: “As of the gazelle and as of the deer” — He compared the disqualified consecrated animals to the gazelle and the deer: just as the gazelle and the deer are exempt from the firstborn laws and from the priestly gifts, so too the disqualified consecrated animals.
Derash on the verse (Sifrei) — equating redeemed pesulei ha-mukdashin with ordinary game animals.
Redeemed disqualified consecrated animals are exempt from the laws of the firstborn and from the priestly gifts, like the gazelle and the deer.