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Looks like they’re verifying, through fleet sampling, if the bolts holding the battery on the car are backing out over time. This shouldn’t need paint repair unless they somehow dinged it inadvertently.
I tried to get under the car to see, but I don't have an easy way to look -- if I had a selfie stick, I'd run a video under the car with my mobile phone.
I'd imagine that the paint on the bottom is more for rust protection than anything else since we don't really see it.
Here is a quick video I shot of the underside of the Model 3. It started to rain, so I tried to cover the outer edges in about 30 seconds. Can't really tell much here.