Thanks so much for reminding me of my promise.

Literal

Promise [obj-を] cause-to-remember-[favor-てくれて] really thank-you.

思い出させる is the causative of 思い出す ('recall') — '(you) made me remember.' Combined with ~てくれて, it expresses gratitude for an action done on the speaker's behalf. The ~てくれて+ thank-you pattern is a staple of heartfelt gratitude: '(I'm) thankful for (the fact that you) did X (for me).'