This is joint work with Andreas Stavrou. For a compact orientable surface S of genus g with one boundary component and for an odd prime number p, we study the homology of the unordered configuration spaces C(S) := coprod_{n>=0} C_n(S) with coefficients in F_p. We describe H_*(C(S); F_p) as a bigraded module over the Pontryagin ring H_*(C(D); F_p), where D is a disc, and give a splitting as direct sum of certain well-behaved quotients of this ring. We also consider the action of the mapping class group Mod(S) on the homology, and identify the kernel of the action with the subgroup of Mod(S) generated by separating Dehn twists and p-th powers of Dehn twists. We compare with some partial results about the Mod(S)-action on ordered configuration spaces, obtained in joint work with Jeremy Miller, Jennifer Wilson, and Andreas Stavrou.