I would like to remove the "Unassigned" choice in the "Planned For" field for my defects.

Open the Project Area and select the Process Configuration tab there. You will find a tree-view there where you can find the different WorkItem types under Project Configuration/Configuration Data/Work Items/Types and Attributes. Near the bottom is a list of properties which make up the selected work item type, and there you can also edit the default value or the types of values that are available at all.

I'm not 100% sure about the Scrum setup, but usually you will need the project admin role in order to make these changes.

Depending on what you want to achieve and how you structure your workflow, you could take a different approach though. Instead of disallowing this state, you rather create a custom report that gives your team a list of unassigned defects which you then assign e.g. in the next team meating. This is also more useful if the people finding and reporting defects are different from those that assign them.

Cheers from Hamburg!

Uli