The battery in my key is running low, so I wanted to replace it.

When I opened my key, I noticed a small circuit board located under the battery.

But what is it? Is this original?
I bought the car second-hand.

Originally, it should have a CR2032 battery, but now it had a CR2025 battery.

 

Looks like an immobilizer transponder.

 

I just got a reply from the dealer.
It appears to be part of the anti-theft system. It disables the keyless entry signal after 5 minutes of no movement.

 

Interesting. It probably extends battery life too.

 

It's a smart idea to prevent relay attacks on wireless keyfobs, especially the JLR ones which are a popular target.

There's a few options like this:
https://www.sleepingbattery.com/en/home/

 

That's a lot of money for a battery. Much cheaper to get a Faraday pouch that instantly hides the fob.

 

You can also just disable keyless entry if your car has it. Instructions are below. I did this to mine. I did take me at least five tries to get it to work though.

To disable F-Type keyless entry. Have drivers door open and key inside the vehicle. Press headlamp button three times and then the unlock button. To turn back on same sequence followed by lock button.

Open driver's door (using fob)
Key fob inside car.
Press headlamp button on the key fob 3 times.
Press unlock button on the key fob once.
Keys outside car.
Close driver's door.
Lock car using the fob.
Unlock car using the fob