A.T. Robertson Commentary Galatians 4:17

"They zealously seek you in no good way; nay, they desire to shut you out, that ye may seek them." — Galatians 4:17 (ASV)

They zealously seek you (ζηλουσιν υμας). Ζηλοω is an old and a good word from ζηλος (zeal, jealousy), but one can pay court with good motives or evil. So here in contrast with Paul's plain speech the Judaizers bring their fawning flattery.

To shut you out (εκκλεισα υμας). From Christ as he will show (5:4).

That ye may seek them (ινα αυτους ζηλουτε). Probably present active indicative with ινα as in φυσιουσθε (1 Corinthians 4:6) and γινωσκομεν (1 John 5:20). The contraction -οητε would be -ωτε, not -ουτε (Robertson, Grammar, p. 325).