A gift can be deleted from the Gifts Grid in the Fundraising Module by selecting that specific gift and clicking on the trash can icon. If the icon is not showing on the left side of the grid, it may be located on the far right side of the grid at the end of the record. 

You will get a confirmation message asking you to confirm that you really want to delete the gift. You can cancel or click OK and the gift will be deleted.

Gifts are deleted in the same way in the constituent's record under their Gift Tab.