Greetings cb200732,
Thank you for using Apple Support Communities.
I understand that you share a calendar on your devices, and you are unable to edit a calendar invite on your iPhone. You can edit the calendar invite on your MacBook. So, the issue seems to be isolated to just the iPhone. I definitely know how important it is to make sure that you can use your calendar with no issues when using any shared device. I'm happy to assist you in finding the best resolution to this issue.
First, close all apps on your iPhone, including the calendar app. The article Force an app to close on your iPhone, iPad, or iPod touch will help, specifically, this section:
When you double-click the Home button, your recently used apps appear. The apps aren’t open, but they're in standby mode to help you navigate and multitask. You should force an app to close only when it’s unresponsive.
Here’s how to force an app to close.
Double-click the Home button to see your most recently used apps.

Swipe right or left to find the app that you want to close.

Swipe up on the app's preview to close the app.

Once you've close all apps, please use the following article and give your iPhone a fresh restart:
Restart your iPhone, iPad, or iPod touch
After you've closed all apps and restarted, see if you get the same result when editing a calendar invite on your iPhone.
Best Regards.