Aha, the dreaded Uni Paint Markers. I've had reason to curse these myself over the last few years as I once had a postgraduate student who was fond of writing on special petri dishes with the pens. These are all oil-based markers.
OK, the first thing I'd recommend you try is something the Americans call Rubbing Alcohol. Its chemical name is Propan-2-ol or Isopropyl Alcohol. Now this stuff is extremely inflammable, has a relatively low flash point and is poisonous so you may have problems obtaining it but it's used in tremendous quantities by chemists everywhere. If you can obtain it or take the photo to someone who's prepared to try it for you, it should be applied to the photo with gentle rubbing on a Q-Tip or similar. It may well work.
The second thing you could try is lighter fluid again applied with a Q-Tip.
Failing that and only as a last resort, the ink should be able to be removed by using petroleum distillates. These were formerly known as hydrocarbons and are extremely inflammable, toxic and sometimes carcinogenic chemicals. There are many of them that would work such as toluene or xylene but in general, but you will encounter great difficulty in sourcing them as they are again normally only used under laboratory supervision due to their toxicity, carcinogenic properties and low flash point.
I know that toluene works, because I've watched a technician cleaning the ink off with the stuff in a fume cupboard, but then I've got the advantage of having university laboratories well stocked with these chemicals.
If you know a friendly industrial chemist, scientist or chemistry school teacher, have a chat with them; don't try to source or use these very dangerous hydrocarbons yourself.