A subgroup effect that is significant for one group only

A signal's effect is estimated within two market regimes. In regime A the effect is $4.0$ bp with standard error $1.5$ bp ($z_A \approx 2.67$, $p \approx 0.008$, significant). In regime B it is $2.0$ bp with standard error $1.6$ bp ($z_B \approx 1.25$, $p \approx 0.21$, not significant). A researcher announces, "The signal works in regime A but not in regime B."

Test whether the effect genuinely differs between the two regimes, and explain the error in claiming a regime interaction from the two separate p-values.