EL AL Matmid - Connecting in Madrid - What happens to baggage?

I'm going to be connecting in Madrid from an Iberia flight from JFK, to an El AL flight from Madrid to Tel Aviv. What happens with checked baggage?

Does it just get transferred automatically? Do I need to claim it in Madrid and re-check it / go through El AL Security Landside? Or is there some other procedure?

you can check it all the way to TLV.
In MAD near the elal gate the security people interview you and they will decide what other procedure the luggage has to go thru.
It's better to have a combination lock, this way you can give them the number and don't have to give them the key.

Is it a single booking? Where did you book the ticket?

Yes, it's a single booking, it was booked through American Airlines reward reservations.

Then you're fine. Bags will be checked through.