in my opinion, i'd give them multiple levels of information. give them a simple notice that they're submitting score information, and provide an option to view more detailed information if they wish.
I agree, I'd suggest with Terms & Conditions there are:
1) people who don't read/skim them (the majority)
2) people who want all the details (a vocal minority)
So if your T&C's state something like 'we may send puzzle data to our server, where it might be stored' & you also have an FAQ on your website with the full details that should satisfy both.
I would second this opinion. Anyone who cares about the detailed information surely understands the need for simplicity, and will only be annoyed if you're intentionally misleading.