Is there a defence to a 3-3 invasion to a 4-4 open?

I’ve seen it a few times lately, where I’ll open with a 4-4 in the corner and a little while later, my opponent will invade on the star point and steal the corner.

Ex from a recent game: move 48

I’m wondering if there’s a joseki or something that involves fending this off, or at least keeping some of the corner territory and not having to switch to a completely influence based tactic.

In that particular game, you should have killed your opponent because your stone already had friendly support. If there is no support, the invasion is supposed to live and you get outside strength in compensation. I left some variations in the review of your game.

If you hate this invasion, play more 4-3 stones in the opening or play supporting stones for your 4-4 stones so that they cannot be invaded anymore.