He told Hull's official website: "I must admit that I did look for our games against Scunthorpe when the fixtures came out.
"I've got to go back there some time and hopefully the fans will be receptive towards myself.
"I've always said that I enjoyed my time there but I think I was ready for a new challenge.
"The fans at Scunthorpe were great to me and hopefully they appreciate that I earned the chance to move on.
"But if they're not then so be it. At the end of the day i'm a professional footballer and will just get on with the job."
Dawson joined Scunthorpe from Nottingham Forest for £50,000 in 1999 after previously coming to Glanford Park on loan.