Dear Fiona,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
As per your description, we're sorry to hear that you are having issue with Teams assignments on iPad, and you've tried Teams reinstallation and clearing cache. For the situation you encountered, we do understand the inconvenience caused and apologize for it.
Considering that you've tried most of the troubleshooting steps user can do on iPad, we're afraid that more resources need to be involved in to help further.
On one hand, please restart iPad and open Teams web app in browser to check if you can mark assignments in web app as a temporary workaround.
On the other hand, we sincerely recommend that you contact your Microsoft 365 administrator and follow the steps in this article to create a support ticket with online support. The support team there has higher permissions than us, they help check the situation on your end, dedicate more resources to collecting logs, and help you troubleshoot. The support engineers there also have the correct escalation channel, and this is the most efficient way to report such issue.
For reference, how do I find my Microsoft 365 admin?
Please accept my sincere apologies for not being able to resolve the problem and for redirecting you to the related development team. I regret any inconvenience this may cause. The fix to your concern can be identified through the background logs, and I suggest you raise a support ticket from the Office 365 admin center, where the related team will investigate the problem further by collecting the necessary background logs.
If there are any updates or we don't understand you, please feel free to let us know.
Once again, I apologize for the inconvenience this has caused. We appreciate your patience and understanding and thank you for your time and cooperation.
Sincerely,
Rhoda | Microsoft Community Moderator