Lexical Definition

‎καίτοι‎ kaítoi (kah'-ee-toy) and yet/although G:CONJ
from ‎καί‎ and ‎τοί‎

although.

Abbott-Smith

** καίτοι (= καί τοι, and so also written in cl.), concessive particle, [in LXX: IV Mac 2:6*;]
and yet, although: Ac 14:17; c. ptcp., He 4:3.†

Abbott-Smith References

Book Refs
Acts 14:17
Hebrews 4:3

Liddell-Scott-Jones

combination of: τοί (καί+τοί)

καί τοι,

and indeed, and further, frequently in [Refs 8th c.BC+] with one or more words between, [Refs 8th c.BC+]; καὶ τἆλλά τοι [Refs 8th c.BC+]

__II after [Refs 8th c.BC+] usually, and yet, to mark an objection introduced by the speaker himself, frequently in Rhetorical questions, καίτοι τί φημ; [Refs 4th c.BC+]; κ. τί φων; [Refs 5th c.BC+]: without a question, κ. φύγοιμ᾽ ἄν [Refs 5th c.BC+] is falsa lectio in [Refs 4th c.BC+]; so καίτοι περ variant in [Refs 5th c.BC+]
__III with a participle, much like{καίπερ}, [Refs 5th c.BC+]: once in the Attic dialect Oratt., [Refs 5th c.BC+]