It definitely refers to the figures, as that is the subject of the clause that follows "although entirely unexpected".
It can semantically not refer to the firm, as that would mean the firm was unexpected, which seems to make less than a little sense.
If you want to convey that the firms good reputation was unexpected, it would be much clearer if the sentence would have been differently formulated, for instance:
notwithstanding the figures being incredible, they were obtained by a market research firm with an unexpected impeccable reputation.
You could use unexpectedly as well. Unexpected modifies reputation, unexpectedly modifies impeccable.
Reading the sentence again and again, and trying to formulate a simpler one, I agree it could refer to the reputation, although I fail to see what mechanism causes that.
Although entirely unexpected, the creatures came from a red planet.
In this case there seems to be an obvious implication that we might have expected creatures from a blue planet, but not from a red one.
In that interpretation, though, it is the fact that the figures came from such a firm that is unexpected - not the fact that this particular firm has such a reputation.
So instead of saying:
It was unexpected that the firm would turn out to have impeccable reputation.
I would say
It was unexpected that such a reputed firm would produce these figures.