How do I change the local path of a subfolder in TFS (not the whole workspace)?

If you want to change the local path for the working directory of the Team Foundation Server (TFS), you need to go to File -> Source Control -> Workspaces (File -> Source Control -> Advanced -> Workspaces for VS2017), then select your workspace (it should match your computer name) and click Edit.

In the next dialog change the mapping for the root TFS node to the new location on your hard drive. You need to perform a "Get" on the whole TFS tree to update project associations.

There is the issue in Source Control explorer, there is a feedback: Manage Workspace Issues - Changing the Local Path of a Project.

You can get the latest version by clicking Get Latest Version (your screenshot), then the files will be in the correct folder and the cache will be updated, then you will find the path is changed in Source Control explorer.

For VS2017 you can change local path from File -> Source Control -> Advanced -> Workspaces... In the manage workspace dialogue box, you need a select row of which contains your computer name, then edit it and change the local path.