The only time TPMS needs to "learn" anything is when you replace the sensors. You didn't. So there's nothing to learn. I have trouble believing your batteries are dead. My '07 Acura's sensors are on the same batteries it shipped with, and are showing no signs of draining any time soon. TPMS is an incredibly low-power system that does not send a continuous or heavy datastream, so the power use is about as close to nil as you can get.
BTW, you can get a new TPMS sensor for 23 bucks. So not only did they break your sensor, but they want to charge you labor to fix the mistake.
I think the tire shop messed up your sensors.
Having missed the part where it took a week for them to come on, I'm still suspicious as to the lifetime of your batteries. I would take it to the dealership and ask them. Unless you drive a lot you're probably even still under warranty for them.