Interpretation of Peirce's realism which grew out of combining Kantian epistemology with scholastic ontology of Duns Scotus (Peirce calls himself "a scholastic realist of a somewhat extreme stripe") is indeed difficult. What makes it even more difficult is that Peirce went through several major reworkings of his "architectonic" without clearly indicating what was kept and what was revised, so it is easy to find statements in his works that appear to be contradictory. It is fair to say, however, that he flatly denies the intelligibility of "things in themselves", as did many others starting with Fichte, "there can be no concept of absolutely incognizable since nothing of this sort occurs in experience... Hence a term can have no such meaning".
But Peirce also rejected Kant's identification of things in themselves with noumena. Pihlström in Peircean Scholastic Realism and Transcendental Arguments argues that Peirce can be understood as naturalizing and pragmatizing Kantian transcendental arguments, and his noumena are projections of "pure reason" downgraded to fallible human knowledge. Due to Kantian scruples Peirce can not adopt a metaphysical realism with already conceptualized world "grasped" by the mind (he rejects what is now called the myth of the Given). On the other hand, he wants a robust notion of truth answerable to independent and demystified reality. The result is a dual picture of reality, first as non-conceptual and encountered through action and reaction (pragmatism), and second as conceptualized through such encounters but only "at the end of inquiry". The inquiry may involve multiple human generations, and potentially even non-human beings, and may never be achieved in actuality, Peirce defends reality of possibilia. The truth is identified with this "final opinion", hence it is not a correspondent truth in any traditional sense. And it is this final opinion that hosts the noumena:
"There is a definite opinion to which the mind of man is, on the whole and in the long run tending. On many questions the final agreement is already reached, on all it will be reached if time enough is given... This final opinion, then, is independent, not indeed of thought, in general, but of all that is arbitrary and individual in thought; is quite independent of how you, or I or any number of men think. Everything, therefore, which will be thought to exist in the final opinion is real, and nothing else...
This theory of reality is instantly fatal to the idea of a thing in itself, - a thing existing independent of all relation to the mind's conception of it. Yet it would by no means forbid, but rather encourage us, to regard the appearances of sense as only signs of the realities. Only, the realities which they represent, would not be the unknowable cause of sensation, but noumena or intelligible conceptions which are the last products of the mental action which is set in motion by sensation". [CP 8.12-13, emphasis Peirce's]
Margolis in The Passing of Peirce's Realism rightly points out that in the absence of metaphysical guarantees it is unclear why the inquiry should converge on any "final opinion". Peirce himself moved from certainty about this to merely "hope" in late years. Aside from being written off as "19th century optimism", the usual defense is pragmatic, this convergence is merely a hypothesis, as the entire corpus of science is hypothetical, albeit confirmed by practice. This is not far from Kant's regulative ideas or neo-Kantian "limit concepts".
Pragmatism even allows Peirce to offer hypothetical metaphysics, which connects his remote noumena to the acting/reacting reality of everyday encounters, see Haack's "Extreme Scholastic Realism:" Its Relevance to Philosophy of Science Today. It posits actions/processes at the core of experienced reality (Secondness), objects are viewed as their conceptual derivatives, and it construes "generals", relations and laws (Thirdness), as manifested in the patterns of actions/reactions. It is they that are the fundamental reality for Peirce:"All that Hume attacked I defend, namely, law as a reality", this is why he calls his realism "of extreme stripe". This relational ontology might raise concerns familiar from dealing with Platonic froms, infinite regress on relations of relations, etc. But for Peirce only some generals are real, which ones is for empirical science to hypothesize and confirm in action, it is not a business of a priori Platonic contemplation with its pure mathematical largesse.
Pihlström suggests that one world/two perspectives (a.k.a. dual aspect) interpretation of Kant is more favorable to finding common ground with Peirce than the traditional phenomenalist interpretation that Peirce accepted. Indeed, this reading is more hospitable to realism since appearances are already real and things-in-themselves are just another aspect of them. Two key differences still remain however. First, Kant's picture is static, we have a fixed transcendental subject confronting a fixed world dressed into a straightjacket of reason's own fixed a priori categories and schemata. There is little epistemic movement in this world beyond clarification of the obscure. Kant can not therefore make the use Peirce has for noumena as happy limits of epistemic evolution, they are static empty posits.
Second, Kant's view of knowledge is absolutist, nothing short of apodictically certain passes the muster, not metaphysics, not chemistry, not psychology. On this standard the chasm between phenomena and noumena is indeed unbridgeable. But on Peirce's pragmatic view even mathematical certainty is fallible, and its difference with the empirically scientific one is of a degree, not kind. Even the "a priori" that frame phenomena are neither a priori nor immutable, they are merely high level hypotheses to be revised eventually. So what Kant cast out as less-than-knowledge aided by practical reason and reflective judgment, is now admitted in full and paves the road from phenomena to noumena. On Peirce's optimistic "hope" the two perspectives merge in the "final opinion".
