ὑποδεξαμένη, having secretly (ὑπό) received them as guests. In Hebrews the simple verb δεξαμένη is used.
ἐκβαλοῦσα expresses energetic action, eagerness and impatience in sending them at once. See Mat 9:38 ὅπως ἐκβάλῃ ἐργάτας εἰς τὸν θερισμὸν αὐτοῦ. Mar 1:12 καὶ εὐθὺς τὸ πνεῦμα αὐτὸν ἐκβάλλει εἰς τὴν ἔρημον, Mat 11:15 ἤρξατο ἐκβάλλειν τοὺς πωλοῦντας κ.τ.λ.