There is no such method. The only reliable way to "fix" a backdoored RNG is to mix its output with another, secure RNG.
Specifically, let's consider a backdoor similar to that described by Becker et al. (2013), which essentially transforms the Intel TRNG into a deterministic PRNG using AES in OFB mode, with a 32-bit initial seed (occasionally reseeded) and a fixed key chosen by the attacker.
Between reseedings, the output stream of the compromised RNG is completely determined by the initial seed, which can take only $2^{32}$ distinct values. Thus, an attacker who knows the hidden key can, after observing only slightly more than 32 bits of the output, look them up in a database to recover the seed (or just iterate through all possible seeds to find the correct one).
Alternatively, if the RNG output is used, say, to generate an public/private key pair, an attacker who knows the hidden key and the keypair generation method can easily generate all the possible keypairs and check which one of them matches a given public key.
The important point to realize is that no amount of deterministic post-processing can prevent these attacks — the attacker just needs to incorporate the same post-processing into their own output generation code. The only thing that can stop such an attack is the addition of some other source of randomness, not predictable by the attacker, to the output.
(Actually, if I read the Becker et al. paper right, the specific attack they describe can be thwarted even without any external source of randomness, simply by feeding the compromised RNG output into a sufficiently large (e.g. 128-bit) entropy pool. The reason this works is that their attack does still allow about 32 bits of true randomness to be output whenever the compromised RNG is reseeded, and mixing this into a non-compromised entropy pool will build up a considerable amount of randomness over time. That said, presumably their backdoor could be modified to leak even less actual randomness into the output.)
