We establish some general relations between Heegaard-Floer-based contact invariants. In particular, we observe that if the contact invariant of large negative, respectively positive, contact surgeries along a Legendrian knot does not vanish, then the Legendrian invariant, respectively the Legendrian inverse limit invariant, of that knot is non-zero. We use sutured Floer homology and the limit constructions due to Golla and Etnyre, Vela-Vick and Zarev.