I can't help but think they may have a point that Blair may not be the best person for the job.
I don't know how true the Hamas statements about him not being honest/helpful are, but even putting them to one side he seems a bit of an odd choice.
Surely, if you want to send an envoy in to help the conflict, that envoy should be visibly impartial. Even if Blair takes a totally unbiased stance in the future, his actions as Prime Minister haven't exactly made him look particularly Arab friendly.