Is there a way to modify the values that are currently in the Activity dropdown for a Task work item? Here's the current list:
Sure, you have to edit the Process Template or the Work Item type of the existing Team Project you want to change.
This article gives you information about how to edit a Process Template.
If you want to edit the Work Item of an existing team project is almost the same process, only the start is different as you have to select this command:
Once your Task Work Item Type is selected, double-click on the Activity field in the Fields tab.
Then in the windows that opens, go to the "Rules" tab and double-clik on the "SUGGESTEDVALUE" line.
Then change the lines you want.
Finally save the Work Item type, if you're from the process template then follow the procedure told in the article, if you're from the Work Item in an existing Team Project, you just have to save for the change to be effective.
BUT, beware (for the existing Team Project case) that if some Work Items already exist in your Team Project that use a value you removed, these ones will generate an error the next time you'll edit them. You'll have to change the value of the Activity field to an existing one if you want the Work Item to be save-able.