Why would the alleged cause of the problems react to a letter from a downstream buyer?
I never said they would react to it. However, Kroger does not have to react to alleged problems at one of their suppliers until they have been proven in a court of law. So if you feel the need to write a letter so that you feel like you have "done something", it's a waste of time to write it to Kroger and you might as well just address it to the supplier.

If these allegations are true, the supplier is the one who has to change their ways and improve the working conditions of their employees, not Kroger. Isn't that what you want - the employees to be able to have employment and a harassment-free workplace? Or do you just want Kroger to terminate them and cause their employees to have to look elsewhere for work?

BTW, if you had read the EEOC court filing, you would know that the complainant could not even provide the name of the co-worker who was allegedly sexually harassing her. Something doesn't sound right, surely she would know [[or could find out) the name of the person was bothering her.