Notes. The constraints relate to parameters given in Gaia DR3 data tables gaia_source and vari_cepheid. Astrometric constraints (Descriptions available here: https://gea.esac.esa.int/archive/documentation/GDR3/Gaia_archive/chap_datamodel/sec_dm_main_source_catalogue/ssec_dm_gaia_source.html) are applied to all Cepheids used in this work and reproduce the sample of Cepheids used by Riess et al. (2021). astrometric_chi2_al quantifies the goodness of fit in the along-scan direction without taking into account astrometric_excess_noise. Positive values of astrometric_excess_noise indicate that the source may not be astrometrically well behaved, and this excess noise may be relevant if astrometric_excess_noise_sig > 2. Since currently, a detailed guidance for how to use these parameters is lacking, we adopted very conservative cuts to remove the clearest outliers. Photometric constraints are applied only to the sample of Cepheids for which Gaia photometry is used. In particular, the parameter ipd_frac_multi_peak specifies the percentage of multiply peaked Gaia windows that were accepted by the image parameter determination. We adopted a constraint in this parameter to avoid blending of the Cepheid photometry with nearby sources, which particularly applies to the Bp and Rp spectrophotometry. An overview of these samples is given in Table 7.