Ordinarily, Percy and Grog don't really interact very much, save for the occasional small conversation here and there. Grog acknowledges that Percy is an intellectual, and in turn Percy typically finds Grog charming after a fashion.
"Desperate Measures" (4x02), however, involved Grog and Percy arguing about what to do with a githyanki skull with a jewel embedded in one of its eye sockets. Inside the jewel was a creature that promised to grant a wish if it could be released. Because Percy and Grog wanted radically different things, the two of them nearly came to blows.
Still, they both value what the other brings to battle and save for that isolated event the two of them are cordial with one another.
In "Trust" (6x01), while Percy tries to get his guns and ammo back from Grog, who's trading them all for random items Percy has, Percy offers to give Grog a 'title' in exchange for all his guns. Grog accepts and gives them all back. Percy then gives Grog the fake title of "Grand Poobah de Doink of All of This and That". This may partially be Percy's revenge on Grog for taking all his weapons. Far from being upset, however, Grog seems very pleased with his title.
In "A Bard's Lament" (7x01), after Grog leaves Scanlan's room, he finds Percy in the hallway. Though they share a stilted conversation, Percy asks if Grog knows he's family. Grog responds with saying that he "doesn't know much, but [he] does know that." Percy said he was glad to have an older brother again.