I heard a claim that Jews in Gaza do not keep Shmitah because it is not actually biblical Eretz Yisrael. Is this true, and what sources can I use to refute it if not?

Gaza was outside the boundaries of Israel that Jews succeeded in settling at the time of Ezra and Nechemya and it was not sanctified at that time with the kedusha of the agricultural commandments. It is unquestionably included within the Biblical boundaries of Israel - those boundaries that we are commanded to include under Jewish sovereignty. Confirm this for yourself by looking at the end of Sefer BaMidbar.