The correlated remainder is only in the vicinity of the signal event.

The 2nd team is arguing the presence of residual correlations after the signal is removed means the total correlation isn't well described by a gravity wave signature.

This is experimental data, so there's clearly going to be noise and there's clearly going to be complexities in the detector response to the event. The question boils down to whether the residuals are significant enough and distinct enough from expected detector response behaviors to call the detection into question or suggest something unexpected is contained inside the detected signal.

It all boils down to what they subtract. It is said that they subtract the wave signal. Is this signal known for sure or very predictable ? It also depends on how they subtract it. Is it in the fequency domain or the space doman ? I didn't read the arXiv article and don't plan too. Just commenting and asking.

Think of it as a matched filter tuned to the impulse response of a gravity wave. If that filter matches the observed signal then it's a detection, if it doesn't then it's not. The debate is over the significance of the inevitable remainder after subtracting the model of the signal. Is it an expected amount of remainder or an unexpectedly large amount of remainder.

If any correlation in the residual signals would be enough to doubt the discovery then I don't understand why they didn't simply combined the signals into one by minimizing the residual correlation.

Your suggestion to just minimize the residual correlations would unfortunately boil down to "analyze the data in the way that best hides any problems in the data" which isn't what anyone wants.

There are specific signal shapes/characteristics that would be producable by a gravitational wave. Anything that doesn't match that shape/doesn't have those characteristics by definition isn't from a gravity wave. Ignoring those characteristics and just saying "if it's correlated it's from a gravity wave" would be a highly incorrect way to analyze the data, which is why none of the scientists in the debate would advocate doing that.

I'm not advocating that any correlated signal should be considered a gravitational wave. I'm just saying that, if residual correlation is such a problem, then it would make more sense to create a combined signal by minimizing the residual correlation.

This discussion would then simply be about how well the combined signal matches a gravitational wave, which seems a lot more sensible.

I suspect they did that in part, but it's also critical to keep the signals distinct precisely because you expect the noise to be uncorrelated between the two signals so you're introducing an additional square root of two gaussian noise factor in the combination.

This sort of thing is much more about statistics and error propagation than one encounters in more traditional signal processing.