The headword, evidently extracted from somewhere, is aorist active infinitive of paleu/w. LSJ s.v. registers both the primary (wrestle) and the applied (decoy, entrap) senses of it.
[1] Eudemus s.v. paleu=sai (= Photius, Lexicon pi64 Theodoridis, with other references there), who also provides the first sentence after the quoted proverb (see n. 3).
[2] Not in the paroemiographers.
[3] This is also in Eudemus (see n. 1) with different punctuation.
[4] A paraphrase of Aristophanes, Birds 1083 (web address 1), with scholion; cf. eta 290, phi 381. Aristophanes has called the birds in question just "pigeons" (line 1082: ta\s peristera/s); the commentator may be taking the opportunity to explain why some pigeons are called "wrestlers".