The Twyleth Teg are probably Wildfae, neither Summer nor Winter nor a member of the Accords. They are hereditary enemies of the Fomor, so this was a score settling, nothing more and the head a message “see our long term enemy who has thwarted us and kept us down for centuries, that’s his head that is, so when we say we can take you all, you better believe it”
Agreed; my suggestion is that Nudd's death was claimed by the Fomor (and by extension, in theory, the Black Council/Outsiders), and this suggests a parallel to the assassination attempt on Etri (unless that was something more convoluted, which might break the parallel) being ultimately sourced in the Fomor/Black Council/Outsiders.
I'm not necessarily suggesting that Thomas is Nemfected; he was likely a patsy. But his controller would have been connected to Team Outsider, as opposed to various other theories, like "Eb coerced Thomas into attacking Etri as an attempt to get rid of Thomas, in order to protect Harry."
(Something that cuts against the parallel is that I think Mab was aware of the attack on Etri either a bit before or immediately when it happened, but she seemed to be surprised by the death of Nudd. It doesn't necessarily destroy the parallel, but I thought it was worth noting.)
...And now I have a new theory! One of the other mysteries were "who controls the cops/FBI that were watching Justine." ...Has anyone seen the Erlking recently? Since, you know, two other heads of Wyldfae courts were just attacked, and one killed?