Hi John,
Too bad to see that. Well, the answer on your question is very simple. It can happen the same way as with any other compact camera with zoom lens. Because the GXR modules are nothing else than small cameras without the body

It just happens much less frequently than in cameras with the lens mount. Try to search the internet about the dust inside the compact cameras. It simply happens.
The lens is extended/retracted every time you turn the camera ON/OFF (not to mention zooming). In these cases, the lens tube works as a small vacuum/dust pump. And of course, the problem could get worse in case the unit/camera is carried in a pocket without any kind of protection. Pockets are full of dust and threads. So it's not surprising to see such a problem, especially in pre-owned camera. On the other hand, it would be very surprising to see such a problem in fresh new unit.
BTW, I already noticed one dust spot in A12 50mm. So even these modules are not so dust-proof as suggested by Ricoh marketing. But it happened after 1 and half year of very intensive and crude use, with module often carried in a pocket. So it's not that bad result? I never expected the modules to be completely dust proof. It's simply impossible to make such sealed module as long as the lens is extending/retracting.
I would suggest you to ask Ricoh for repair. All P10 modules are about a year old so there is a big chance your module is still covered by a warranty? The Ricoh service partner in the US is Criscam. The only problem is, they don't have the GXR body and modules listed in the list of supported cameras

But there is still a way to ask them what to do.
Go to here:
https://www.criscam.com/register_ian.php
In the "Type" field select "
Digital-compact camera", in "Make" select "
RICOH" and finally, in the "Model" select "
Model not shown here". After that, there should appear a popup window with a form where you can type your request.
Eventually, you could contact them via these numbers and email:
C.R.I.S. Camera Services
Phone: 480-940-1103
Fax: 480-940-1329
Email: <ricoh@criscam.com>
Hope this helps?
Hope this helps?