Jonas, 21, and Greene, 23, went out for dinner at Ichiban Japanese Grill & Sushi Bar in Baton Rouge, Louisiana.
One of the managers at the restaurant told People.com: 'They were really friendly.
'They just walked in, sat down, and the word started going around that they were here. They each had a Hibachi meal and some sushi.'
The manager added: 'The kitchen crew and wait staff were excited to see them. Some of them stayed late because they were hoping to get their picture.
'I don't watch the Twilight movies, so I wasn't so familiar with them. But everyone else in the restaurant knew who they were.'
The manager added that they seemed very nice together as a couple.