A cell phone would be utterly useless without the proper infrastructure--which hadn't been invented yet, and can't exactly be hauled back in a Delorian.
The resolution is nowhere near clear enough to say that she's holding anything at all. People talk to themselves, people put their fists/knuckles/hands to their chins/cheeks/temples/foreheads when thinking. She could have had a toothache, or an earache, or been using a hearing aid. She could have been holding something against her face, something cold/hot/soft/whatever for some purpose. She could have been stung by a bee and been muttering about it while clutching the afflicted area. She might have cut herself shaving her grizzled sideburns and been holding a lump of coal to staunch the bleeding. She might have been slapped by an enraged chimpanzee in a bell-hop costume after feeding him a maggoty bananna she purchased from a disreputable street urchin turned produce vendor.
Sadly, none of my examples are even close to as absurd as this buffoon's. A "time traveller using a cell phone"? Feh! Why not just tell us it was a lepercaun riding a unicorn down a rainbow from Asgard? Guys like this give a bad name to folks who study the real riddles of our world's frontiers, our dust-obscured and largely unknown past, and the cosmic riddles born of the vastness of space. He makes it too easy for the Phillistines to point at them and laugh "Look at that looney! He thinks Atlantis might be based on a legend common throughout the ancient world, next he'll say there was a cell tower on the Sphinx's head!"
