Deformations and parity
Metric is parity-even, and NSNS -field is parity-odd
The RR 1-form and 5-form are parity even, and the RR 3-form is parity odd.
Dilaton is parity-even
Nonphysical deformation which we considered is parity-odd, and the deformation of BRST operator is also parity-odd. Therefore it appears that it should not correspond to dilaton.
Conclusion: Trying to understand the unphysical vertex by going to the flat space limit we discovered the "wild" deformations of the flat space pure spinor action, which are equally surprizing.