You can delete an export simply by selecting its name and using the Erase command of the Edit menu (or typing the Delete key). You can also use the Delete Export command (in menu Export).
To remove many exports at once, the Delete Exports on Selected command removes all exports on all highlighted nodes. Also, the Delete Exports in Highlighted Area command removes only those exports that are in the selected area . When an export is deleted, all arcs connected to that port on instances of the current cell (higher up the hierarchy) are also deleted.
To move export text, simply select it and drag it. The location of the text has no effect on the location of the export: moving the text is only for improvement of the display. However, if you check "Move node with export name" in the "Ports/Exports" preferences (in menu File / Preferences..., "Display" section, "Ports/Exports" tab), then moving an export name will cause the node (and the export) to move as well.
It is sometimes desirable to keep an export but to transfer it to another node. If a cell is in use higher in the hierarchy, unexporting and then reexporting deletes all existing connections. Instead, the Move Export command (in menu Export) can be used. Before using this command, two nodes and their ports must be highlighted with left button and shift-left button. The export is moved from the first node to the second node.