You need her phone number and she will call you for a rematch on Thursday nights.
Keep in mind you can't do rematches before you get the 7th badge.
She is "south of Goldenrod and Daycare Center before Ilex Forest. She's in the big grass patch, at the other end of the large narrow puddle."
She will give you the Leaf Stone if she calls you, according to a Reddit page about Leaf Stones in HGSS. She has a small chance to call you every ten minutes.
(Quote from GameFAQs, Picnicker Gina Phone Number)