What should a mother do who took things from her grandmother's shop without her knowledge, and is obligated to return their value, but she does not remember the value of these things? And can their value be returned as a gift?

Your mother must repent to Allah and return what she took to her mother. If it is still remaining, she should return it along with compensation for any نقص (shortage/damage). If it is no longer available, she should return a similar item, or its value if there is no similar item, unless your grandmother forgives her.

If your mother does not know the exact amount, she must make an effort to estimate it in a way that she is reasonably sure will clear her liability.

As for returning the right in the form of a gift, it is safer not to do so to ensure the clearing of her liability.