this is the stupidest plan ever, everyone knows what that jewel looks like, who is going to buy it from some orphan kids not to mention you'd have to prove it was the real one to who ever buys it so you'd need a certified and trust worthy appraiser.
I actually have a ton of questions, like where did the tv come from, who bought that, did it survive the fire, is it stolen? And since TVs and laundromats are in this world, they are somewhat advanced, but these kids cant find any kind of job? really, why not? The only thing available is brothels? that cant be correct since people have died in a recent war there should definitely be a need for laborers, so whos working in those power plants providing electricty for all these tvs and laundromats? Nobody say but child labor laws that little blonde girl was going to work at the brothel and they seemed fine with her age but all the others are said to be mid to late teens and in this world 16 is considered an adult. So really its just a bunch of bums trying to find an easy way out.
Also that Tv was in color, this just leads to more questions