Takeisha Saunders was browsing Father’s Day cards at a Target store in Dallas in late May, looking for something special for her husband of two years, when she found one that didn’t sit right.

The card said “Baby Daddy” in pink cursive script and featured a black couple kissing. Ms. Saunders, 35, said it was the only Father’s Day card she saw with a black couple — a feature she was looking for to reflect her own family.

The card perpetuated a stereotype, Ms. Saunders said. “Baby daddy” is a phrase commonly used to refer to a father who is not a husband or current partner of the child’s mother.

“My reaction was just, ‘This is my only option?’” Ms. Saunders said on Saturday. “I don’t view him as my ‘baby daddy.’ I would not call him that. That’s offensive to him and me.”