I'm not understanding some basics here. It's an apple product is it not. You have a bill that proves you bought it on a certain date and your warranty is still valid.
Why is there this requirement of serial# in the first place ?
Yes, i can see its quite
small
No software utility that can query this number if the keyboard is plugged in ? to rely on some printed number and expecting it to be legible after a period of time is unrealistic.
This isn't apple you're dealing it btw its some 3rd party service centre contracted to do warranty for apple