Must a girl inform a suitor about the scar from a surgical operation on her back, knowing that this might affect her chances of marriage?

There is no obligation to inform the suitor of what was mentioned, because it is not among the defects that establish the option of annulling the marriage.

It is advisable to choose a person of strong faith and good character, as this is more likely to bring happiness to the wife. Moreover, seeking advice (Istishara) and performing the prayer of guidance (Istikhara) are among the means to achieve success.