Ṭuhāt is the plural of *ṭāhin/ṭāhī* (“cook”), from ṭahā yaṭhū, “to cook.” It identifies those engaged in preparing food, not those merely pursuing animals.
Ṭuhātu l-laḥmi is an iḍāfah: “the cooks of the meat.” It serves as the subject of ẓalla, a verb which, in a past narrative, can convey the continuation of an activity or state.