It appears there is no way to replace the battery. If the sill is aluminum and is adhered by VHB tape, then removing them for a battery change would likely bend and ruin them. Since powered with battery it's not a matter of IF the battery dies, it's a matter of WHEN. For this reason, the illuminated door sill is not a good buy. I think Tesla could have tackled this in 2 ways.
#1 - make the illuminated sills a bit deeper so that they fill that gap between the original sill and weather seal. Then they could hide a power wire in the weather seal and tap power via split connector to the puddle light.
#2 - If going the battery route, then make it out of a resin or plastic type material (something invisible to Qi charging) and embed a wireless Qi receiver in the illuminated sill. Then use VHB tape to adhere a Qi charging pad under the door (these things can be made very thin) that lines up with the charging receiver when the door is closed. That way the sill charges whenever the door is closed.