Is ZenDesk a legitimate Apple contractor?

It's adware. Download and run the free version of Malwarebytes which should get rid of it.

It was developed by a long time contributor to these forums and a highly respected member of the computer security community.

Apple will not pop this nonsense in a browser window or email. That leaves only the crooks trying to convince you that they are either Apple, or an Apple service provider offering to help you out of your identity or bank account. Do not click any buttons on these, not even Cancel. Just Quick Safari.

Run Malwarebytes per Old Toad's recommendation. Then launch Safari with the shift key held down. Then Safari menu : Clear History… all history, and click Clear History. This rids you of history and all cookies set in the browser. Next, Safari Preferences : Advanced panel and [√] Show Develop menu in menu bar. Quit Preferences, and then press option+command+e to clear the Safari browser cache. Quit Safari and relaunch normally.

There is a helpdesk software company called Zendesk which I would normally regard as reputable. This sounds more like a bunch of criminals misusing a legitimate companies name.

Apple certainly would not be using Zendesk to contact you.

Sounds like a real scam to me, any malware may in fact be from them.

Personally I would not trust any such company that makes unsolicited call to offer their services. I would write off such companies as hacker attempting to scammer me.