An employee asked one of the women wearing a T-shirt that read, "marriage is so gay," to turn it inside out to avoid offending others during a recent visit to the Tennessee theme park complex.
The shirt was deemed inappropriate.
The woman complied but later sent an email to the park about the incident.
The park gave them a refund, and Parton responded with a note saying, "Everyone knows my personal support of the gay and lesbian community. Dollywood is a family park and all families are welcome."
The couple, Jennifer Tipton and Olivier Odom, said they were glad to see Parton's supportive statement. They were, however, disappointed that park officials declined to meet with them and a representative from a gay rights organization.
The couple sent a letter to Dollywood officials asking the park "to implement policies that are inclusive of lesbian, gay, bisexual and transgender people; conduct staff sensitivity training; and issue a public statement indicating that the park is inclusive of all families."
The Associated Press contributed to this report.