I have had luck and good results with isopropyl alcohol at 70% (no more). Apply the alcohol on a very soft paper tissue and wipe delicately the back of the backglass. The dirt will stay on the tissue and you will be amazed by the clarity and light coming out of the clean backglass. Change the tissue often and go slow and gently.
I usually finish the process by sealing the clean glass with "triple thick" clear coat by Krylon. When doing the Triple Thick application, you must put regular transparent/magic tape on the clear section of the backglass (score windows). Otherwise, the Clear Coat will not be completely transparent and will disturb the reading of the scores. Of course, that transparent/magic tape must be removed immediately after applying the clear coat and before it dries out. A fine razor blade is ideal for this work. It takes a lot of care to do it well, but it is worth it.
The front can of course be cleaned with any glass cleaner as long as you do not spill it in the back.
Yves