That's where I found & downloaded mine also, as well as the GPG Verification Tool, the GUI one, and double checked the ISO version & keys, the match was 'Not Likely' (or similar wording).
Unlike most other Linux distros, the maintainers doesn't post a SHA256 bit checksum page, which can be copy/pasted in the download manager bot, select the right key type, and allow to be auto checked after the download has completed, the last option will be verification. The Linux MInt Cinnamon breach is why they went to SHA256 checksums, Ubuntu 17.04 has the same, didn't have an issue with that one last night. I prefer the process to be automated, that's the job of the download manager, if only the one who has the ISO (or other download) provides the checksum.
A good LInux user & especially System Administrator will be a lazy one, getting more work done with the least amount of effort. While in practice, I've read more about this on the hardware end than downloading/verifying ISO's, such as having replacement RAM & HDD's inside of needed computers on the job for that 2AM call (common replacements), so as not to be running all over the place looking for these. I'm the same way with downloads, it's a lot of trouble & an unnecessary step to be fooling with GPG keys, especially when the distro maintainer doesn't place the latest version (for Terminal checking) on the page. Plus when using the GPG tool, the ISO & GPG signature files doesn't match.
While 5 years back, I'd not had been concerned over this, today I am, will not run a distro that cannot match it's own signature file, this is a security risk & why the big name ones makes this a painless process for those who prefers the download manager option. That's part of the job of the tool, to verify files as downloaded, although both Linux Mint & Ubuntu offers it both ways, some prefers the manual check. My guess is that if I were to check one of these with the GPG Tool against the provided signature, all would be clean.
Until the issue is fixed, I won't bother again, and am not interested in running dated ones, such as the example page provided. Furthermore, this in far from the year 2013, that was just one year after Ubuntu 12.04/Linux Mint 13 LTS were released, both now out of support. There was another issue, while Peppermint is based in my home State, in Asheville, NC, the largest in the area, part of the GPG sig was from the UK. Is it a UK or US based distro?
The example should be updated to match the last provided release, not one that's unsupported, there was no Ubuntu 14.04 in 2013.
Lastly, and maybe why it ran much better than Windows 8.1 on the 2014 model Dell Inspiron I gave to her, although I maintain there's not a true i7 under the hood (Intel went from producing high performance 1st & 2nd gen dual cores for mobiles, then later quads in the 3rd & 4th gen, now has taken several steps backwards & reverted to 20W duals), it's probably due to Peppermint being an Xfce based distro that it runs as good as it does. Although still not as powerful as any of my notebooks, I believe that model has a low cost, Haswell mobile CPU, which is a reflection of it's price ($799.99 when sold). Based on it's performance, I felt it was more suited towards a child as a first time notebook, rather than one who has been through several that were more powerful & needed for real work.
Hopefully, she has no issues with the Peppermint that I installed, which was the last version released at the time, may have been this one, since I trashed the ISO a few weeks after install, may never know. The family was down on their luck then, as the husband/father abandoned both, fortunately the home was paid off weeks afterwards. I told her that if she ever had troubles & needed to reinstall, or install a newer version to let me know, although at 11 years old, she (Melissa) was responsible, wanted to watch my every step along the way, even helping with the password & the installer in general, so may have learned how to do this on her own. Hopefully won't be doing much photo editing, this requires a powerful CPU & ample RAM (12GB or more). I know that 8GB was installed, because there were 1600MHz modules installed & after checking the CPU specs & seen that it could run 1333 or 1600MHz, swapped for a matched pair of 1333MHz ones I had on hand, why waste high performance RAM on a low end CPU?
I'm also hopeful that the folks at Peppermint will get this key situation in order, this will help the OS to climb the DistroWatch charts, when I took a peek, was performing fairly well for that type of distro. While I don't give just the last 7 days much stock, rather look at the last year as a whole, at each stage. Peppermint has held it's own during this period. No way can a few folks perform a slew of downloads within a course of time to make the results look steady, and why I don't bother with the past week or month's results alone.
There's one notebook that I have that it may run well on, while dated, Xfce based OS's doesn't require a lot of power, and there usually a way if needed, to run on non-PAE based computers, so will need to download the 32 bit version instead, if the devs (wherever located) can get the key issue right. I'd much rather have a SHA256 txt file, so that I can choose the right one for the version downloaded & let the download manger do the work. Example of Linux Mint below, see, one's given two choices.
How hard is the above to perform?