As for any questions why not just mail them ? I have seen a number of physics forums where individual points and queries were raised and the authors were mailed/invited and came on the forum to explain anything asked to the satisfaction of all posters.If you can blow a hole in their theory..do it...publish it or, again, contact them and invite them here as they seem very receptive.
BTW I am not sure about the 1/4 (do you mean the one in the temp calculation? If so that comes from the integration of the energy balance equation to get the temp out) but in response to the 0.7 question their answer was:
The emissivity (e) is related to the albedo (A) describing the reflectivity or the whiteness of an object:
A = 1 - e. In the earlier literature one often finds A = 0.5, in current publications A = 0.3.
In the papers I saw trying to refute their claims it sems this figure is accepted.
Papers (plural)? could you point me to some 'cause I only found one and several "allusions".