In the book, the enchantments in the Lestrange vault at Gringotts resulted in them receiving a number of burns when the objects multiplied and made contact with their skin.
'It burned me!' moaned Hermione, sucking her blistered fingers.
'They have added Gemino and Flagrante Curses!' said Griphook. 'Everything you touch will burn and multiply, but the copies are worthless - and if you continue to handle the treasure, you will eventually be crushed to death by the weight of expanding gold!'
Harry Potter and the Deathly Hallows, Chapter 26 - Gringotts
After escaping on the dragon and disembarking in the lake, they use essence of ditany to treat the burns and other injuries they'd received during the break-in at Gringotts.
It was the first time that he had seen them properly since escaping from the vault. Both had angry red burns all over their faces and arms, and their clothing was singed away in places. They were wincing as they dabbed essence of dittany onto their many injuries.
Harry Potter and the Deathly Hallows, Chapter 27 - The Final Hiding Place
In the movie, this particular part of the book may have been modified to remove the burning, which would cause the scenes following the dragon ride to appear totally out of place. This isn't that surprising since the movies are, on the whole, nonsense and result in a lot of things being unclear.