Now imagine that we swap the stage (2) and (3) such that the extractor feeds the decimator input. What are the implications for the TRNG?
You'll be hit hard with NIST's 800-90B min.entropy calculation for correlated entropy sources. I'm assuming that you're concerned with kosher TRNG's not hybrid models like NIST's DRBG from 800-90A. Those tip out shed loads of pseudo-random bits in-between reseeds (also like \dev\urandom).
That means you need to extract unbiased bits (bias < $2^{-64}$, correlation <$10^{-3}$) from the raw possibly correlated source. Yet you will be aware of the issues concerning NIST's ea_non_iid assessment tool. And there is no other that I'm aware of. So you can't with any authoritative certainty. But you can ascertain whether a source is IID with a high degree of certainty. That's why it is common to either decimate the raw source samples, or adjust the resolution/frequency $(\epsilon, \tau^{-1})$ of the sampling regime instead till IID samples are obtained.
...since it does not change the amount of entropy...
But you have to reduce (so change) the amount of entropy coming from the TRNG's raw source. Otherwise you'll create a hybrid TRNG which produces a large (but pretty much immeasurable) amount of pseudo-randomness in the output stream.
What about other extractors or the use of a PRNG before decimation?
A PRNG cannot compress the samples, so it a PRNG cannot act as an extractor without massive and very inefficient reseeding. And decimation cannot significantly increase the entropy rate, all it can do is convert non-IID samples to IID ones.
You can see this type of conditioning here, where I decorrelate ~21 KB JPEG files to 5.8 KB via some quirky mix of entropy reduction and sampling regime change. In my linked example, I use SHA-512 as an extractor to compress 778 bits to 512 in order to achieve $\epsilon = 2^{-128}$ in accordance with the Left Over Hash Lemma.
