For most purposes faxing documents gives "reasonably" legible copies. Some fax machines can be set to enhance the output [draft, fine and extra fine are some options on some fax machines], try to see if this improves the output. There is also a possibility that through some "glitch" in the phone lines, at the time you sent the fax, output came through indistinctly...try again!
Can you send your screen prints to them by US Mail?