I did not downvote anyone, but Steven's answer and Deltik's comment are incorrect.
SMART is a firmware feature on hard drive, not any operating system or software. The values are generated and accumulated in the hard drive itself. No external software is necessary. Just plug power in, turn it on, and SMART starts watching and logging to it's own NV registers.
There is no well-known way to "reset" them.
You can "disable" SMART in some BIOSes - but again, that has nothing to do with what the SMART firmware is doing inside the drive.
Various SMART-monitoring software and services, can of course be started, stopped, installed, uninstalled. But no commercially available software or power-user tool can arbitrarily change or reset SMART values, and none of them have absolutely anything whatsoever to do with whether the values accumulate.
(But I should add as speculation: the fact that the drive obviously knows how to update them, means in theory that it could be discovered how to do so manually. Maybe there are anti-tamper mechanisms, but since SMART isn't marketed as an anti-fraud mechanism, that seems unlikely. Still, I know of nor have found any way to do so.)
To be clear, some values can self-reset. A surface test with a manufacturers HDD utility - or dedicated commercial software - can, for example, reset some values such as "weak sector count". But only indirectly! I can't find any definitive list of what can and can't be reset, but in my experience most cannot be "reset" by software. Only resettable values via manufacturer intended mechanisms, can reset values intended to be resettable - indirectly, for example via in-drive scan and repair functions.)
In short, unless your Craigslist seller has a Russian accent and lots of bling, the SMART values are almost certainly legit. (And even then that's just racist. Borat showed us that suspicious people from former Soviet-block countries can be adorable, non-HDD-scamming oafs at heart.)
Either way, many SMART values are meaningless at best or misleading at worst (according to BackBlaze and Google.) There are only a handful of values to watch for (source: https://www.backblaze.com/blog/hard-drive-smart-stats/):
- Reallocated_Sector_Count.
- Reported_Uncorrectable_Errors.
- Command_Timeout.
- Current_Pending_Sector_Count.
- Offline_Uncorrectable.
The linked article explains how to interpret the values. Personally, I have a bash script that reports a subset of even those to me, that I run when I suspect trouble.
I would advise running a sequential write benchmarking tool and let it run for a few minutes. (Which will only cover a fraction of the drive.) Then run a random read+write test for as long as you can get away with, this should increase the odds of hitting large trouble spots, and at any rate stress the drive mechanisms more. SMART still may tell you nothing, but the fact that the test continues to run without error should tell you as much as you can reasonably know without having it for 48 hours solid.