This is done in the same manner as you do for removing an activity from an invoice. Open the job which contains that activity and click on the Actuals tab. Then use the scroll bar under that activities to scroll to the right. You will see something like this:
Just click the Check button and click Yes when the confirmation popup appears. This item will be removed from the Check Request and the balance will be adjusted.
This works the same way for removing an activity from an invoice. Just remember that in both cases, you can not put them back after they have been removed. They will have to be in a new check request or invoice as appropriate.