You have to have 50 000 points and 50 cells recorded via CellMapper account to able move towers on map.
On webmap you can just drag and drop tower to new location to improve our map accuracy. Cellmapper will recalculate tower sectors etc after new placement. This will take some time and tower color will change from red to green.
If you delete tower, it will automatically removed from map and reappear when someone record tower data again. You can't revert own actions.