It'll probably take a while though. They're in a pretty tough situation, being basically isolated inside the city.

The only way I can see for Karina to be able to get in contact with the military of touch is either if she gets out of the city, if enough time passes without her entering in contact with the military to justify them sending a small team to rendezvous with her or (the easiest option, but the most taxing to her body) to make something akin to a spotlight with a few of the Jade candles by making something to amplify their light with her ice (and break the distortion enough so ppl can see it from the outside.