Links work on my system but not the clients

Mobile browsers don't support this.  For obvious reasons, only one tab/window can be opened at a time.

<a href="https://example.com" target="_blank">EXAMPLE</a>

Firefox config allows desktop users to decide how links should open -- same tab, same window, new tab, new window.

https://support.mozilla.org/en-US/questions/1226151

Any chance of providing us with the url to the website so we can check the page to see if the fault lies at your clients end or the fault is yours?

Yes it could certainly be a browser cache issue IF you have added the links recently and they still have an old version of the page cached in their browser but then the links probably would not show at all. Have they got an alternative computer they can view the webpage on on or maybe a tablet, smartphone to check if the links are working.