How can I delete those pushbuttons in the toolbar containing no text, only an icon?

You have the following possibilities:

// Delete using the F-key
del P[/8]

// Delete using the quickinfo
del P[Single test]

// Delete using the icon id
del P[@12@]

This requires that you first search for the icon id, either in SAP transaction "icon" or in the GuiXT script editor icon overview)

// Delete the corresponding menu entry with the pushbutton
del M[TEST]