Flight to Baghdad from Heathrow

I posted a question earlier about a problem I had when I travelled to Jordan few months ago.

I had a flight to Jordan from Gatwick to stay few days in Jordan, so at the time my final destination was Jordan. My departure was fine from Gatwick, however when I reached Jordan there were some slight problems that affected my entrance. The problem was is that I used to live in Jordan for 2 years and I left it 2004, when I left it at the borders they told us we wouldn't be allowed to enter Jordan for another 4 years (it's a rule they used to have for people who stay in Jordan and then leave it). When I had my flight few months ago to Jordan at the passport control in Amman airport the issue about the 4 years rule popped up and they seemed to have misspelled my mother's name when I left Jordan in 2004. It took them some time to allow us to enter Jordan. I don't know if the issue still exists.

I've got a flight from Heathrow to Baghdad with Royal Jordanian in few days, this flight has a layover of 10 hours in Jordan. I was just wondering at Heathrow when I check in with the airline do they care if I have any issues in entering Jordan that could affect my boarding? Or do they not look for such issues with passengers? Can they actually see on their computers if I had any issues with a country I'm travelling to when they scan my passport? Same question goes for the passport control at the gates in the airport.

I was thinking I wouldn't have any issues at Heathrow because my final destination is Baghdad anyway and not Jordan, but just wanted to ask you to make sure.