I don't believe that was a destructive recovery. If you did the usual HP recovery manager, it erased everything and wrote the original factory disk partition back onto the hard drive from either CD's or a D: drive partition.
Any of the older files that happened to occupy disk space used by the rewrite would be obliterated, but odds are there will be some files that were just deleted, but not fully erased existing in the free space of your drive. It would take a lot of work, but someone could find them. I doubt that most friends have the skills or desire to do so, especially with a gift laptop, but it's your call.
I read about the
eraser program in another thread and tried it. It has an option where you can erase the free space. with different degrees of thoroughness. I tried it with a single pass where it writes random data. Pretty fast and safe enough in my opinion, unless you expect James Bond's tech support will be reading the drive. Then you want its more sophisticated algorithms, which could take days to finish. I didn't find the program easy to use, but did muddle thru it.