I had written out a few ideas, but thought I should go to the URL to try it myself. When your local site is HTTPS, the URL structure of their code included in your page allows the request to be made via HTTPS - and in this case their HTTPS certificate is rejected by Chrome. There could be something fishy going on, but it's more likely their environment is mis-configured.
Do you have HTTPS on both of your Dev and UAT environments?
Example link:
https://app.moodleanalytics.com/analytics.php?idsite=1234
Additionally, the certificate is 2 years expired:
So, it's probably not you - it's them.