Made a costly mistake with a client's grad photos; lost half the photos — seeking advice

Hey, I'm an amateur photographer and ran into a big mistake. I wanted to post this here because I need some advice and want to hear from people who've been through smth similar.

I shot a graduation session for a client a while back. When I went to deliver, I realized a chunk of the images were missing. My Sony camera rolled over from DSC09999 into a new folder and I only copied one folder when transferring — so those files never made it to my hard drive. On top of that, I've reformatted the SD card twice since the shoot and did other grad shoots, so recovery odds aren't great.

I'm currently running SanDisk RescuePRO on the card. Fingers crossed.

Does anyone have any advice wrt this situation? I still have half the photos from the shoot. Should I offer a refund? I just feel awful especially as an amateur.