Is it obligatory to return a sum of money given as a gift, when it was jokingly told to the giver that it was little, with the intention of increasing the gift, even if the speaker has repented?

If your relative increased the gift after your conversation and she was happy to do so, then there is no blame on you. However, if she gave it to you out of shyness, then it is obligatory to return the increase. There is no specific way to return it; you can insist that she accept it, or use a stratagem to give her the money without stating the reason. But if she did not increase anything for you, then there is no blame on you, because the gift was given willingly by her.