How do I delete a folder that I did not create in SharePoint?

kaseyearhart Contact IT department or site collection administrator for your SharePoint site and request them to grant you contribute or higher permissions in order to delete the folder.

Check this for understanding more about SharePoint permission levels: User permissions and permission levels in SharePoint 

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kaseyearhart 

To delete the SharePoint folder that you did not create, you need to:

1. Make sure you have the appropriate permissions. At least an edit permission will do. 
2. Also, folder deletion can be prevented due to retention policies. Ensure that Retention label policies is not applied to the SharePoint folder. In the situation where you have one applied to the folder, first move or delete any files in the folder that are subject to retention.
3. The site might have exceeded its storage limit. Increase the site quota and delete the item.

For more information, see https://learn.microsoft.com/en-us/sharepoint/troubleshoot/administration/unable-to-delete-files#more-information

https://learn.microsoft.com/en-us/sharepoint/customize-sharepoint-site-permissions

Please let me know if further assistance is needed. You can also provide a screenshot of the error you see whenever you try deleting. Thank you!

Hello kaseyearhart

you need enough rights to delete a folder: https://support.microsoft.com/en-us/office/customize-permissions-for-a-sharepoint-list-or-library-02d770f3-59eb-4910-a608-5f84cc297782

You must have at least contribute rights, or higher. 

Unless it has its own folder permissions, then you need higher permissions.

Best, Dave