Fraction of SNe Ia for one of our simulations (interaction occurring between 500 and 1000 d after the peak) where the CSM interaction was recovered per redshift bin of size 0.002. The simulations are shown for interaction strengths of zero (grey), similar to SN 2015cp (red), and 10 times stronger than SN 2015cp (blue). In the simulation without CSM interaction, the recovery fraction should be interpreted as the fraction of false positives. The simulations with normal ZTF quality reference images are shown with dots and fitted sigmoid functions with solid lines. Simulations where one magnitude deeper reference images were assumed are shown in triangles, with their fitted sigmoid functions in dashed lines.