WA law does allow the "victim" (the store in this case) to compromise with the alleged shoplifter resulting in a dismissed criminal charge.
However, why would the store want to help getting a case dismissed against you? The store was the one that called the police in the first place to arrest you and file charges against you. Some stores have policies not to help defendants in the criminal cases.
Moreover, anything you say to the store's personnel likely can be used against you in the criminal case.
If you do not now have an attorney, you likely should review your facts and options with an attorney.
If your income is low, you may qualify for free or reduced-fee representation by a public defender. The public defender may not have time to call the store for you.
The store likely will be sending you a demand letter to settle its civil case against you. The demand likely is for several hundred dollars.
Having been a Pierce County public defender, I can assure you that, though no doubt overworked, appointed counsel throughout the state make every attempt to work out compromises by calling the alleged victims, if such compromises can be worked out. I personally did this on my cases when with DAC. Several stores will not compromise and there's no sense in asking when it is known that they will not compromise.
Still, compromise isn't the only avenue to dismissal. Depending on whether you have any OTHER criminal history, you may otherwise be eligible for a pretrial diversionary program, such as El Cid. My advice is not to call the store directly, but instead, get an attorney (either hire, or get one appointed) and see what can be worked out through them.