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I'm 99% sure this isn't true. Can you point to a single paper that mentions it?

Edit: actually I'm 100% sure this isn't true. See for example the all sky map from planck (http://www.bbc.co.uk/news/special/2013/newsspec_5106/img/pla...). And a paper discussing how they will measure the CMB dipole using planck https://ui.adsabs.harvard.edu/abs/2002A%26A...393..359P/abst...

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I stand corrected, the current Planck analysis seems to take in account that we are moving through the CMB rest frame although I need to read a bit more. It's a long paper [1]

It was the earlier Planck measurements that did not account for this.

[1] https://arxiv.org/pdf/1907.12875.pdf

This effect seems to be treated and dismissed as insignificant w/r/t the cosmological parameters, in section 3.11 (page 78) of the paper you reference.

There were a lot of new systematic effects in the Planck data, and a lot of the data analysis work amounted to identifying the most significant ones and modeling them out.

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