The closest I can tell is that he'd like to brand him on his hand because of the way he treats his slaves.
"I've got a gang of boys, sir," said the long man, resuming his attack on the fire-irons, "and I jest tells 'em—'Boys,' says I,—'run now! dig! put! jest when ye want to! I never shall come to look after you!' That's the way I keep mine. Let 'em know they are free to run any time, and it jest breaks up their wanting to. More 'n all, I've got free papers for 'em all recorded, in case I gets keeled up any o' these times, and they know it; and I tell ye, stranger, there an't a fellow in our parts gets more out of his niggers than I do. Why, my boys have been to Cincinnati, with five hundred dollars' worth of colts, and brought me back the money, all straight, time and agin. It stands to reason they should. Treat 'em like dogs, and you'll have dogs' works and dogs' actions. Treat 'em like men, and you'll have men's works." And the honest drover, in his warmth, endorsed this moral sentiment by firing a perfect feu de joi at the fireplace.
"I'll warrant ye," said the drover, "holds it and makes money out of it, and then turns round and brands the boy in his right hand. If I had a fair chance, I'd mark him, I reckon so that he'd carry it one while."
Uncle Tom's Cabin