So, your mother took the initiation. Usually people would not dare come to an initiation because you have to sacrifice something, it’s a more serious thing, so then they don't come. But if she took it as a blessing, just sitting there, of course, still it's very good. Even just being there is incredible. Most people don't want to come. If you tell them, they won't come. So, they don't have the karma to have the opportunity. They don't have good karma. That means your mother has created merit just to be there. If you listen, even if you don't understand, it leaves an imprint on the mind. Sooner or later, from that, you get a higher rebirth in the next life.
As far as the Buddhadharma is concerned, just by hearing it, even if you don't understand, you get a higher rebirth. In the next life you are able to understand the teachings so clearly, are able to practice and have realizations of the path and cease the defilements, and achieve liberation. Then, by ceasing the subtle defilements you achieve full enlightenment. Like that, great preparations have been made.
Also, it is amazing that your mother took the oral transmission of Lama Tsongkhapa Guru Yoga. Even if she was just sitting there, and didn't take the oral transmission, or didn't pay attention, it is an incredible advantage, and many benefits are received. Just seeing Chöden Rinpoche, sitting in front of him, is incredible. We see billions of people in New York, but we don't get that blessing or benefit for the mind as when we see Chöden Rinpoche. Seeing him, she gets that benefit, purifying the mind, receiving peace, and that deep feeling. She got that from somebody who not only has the realization of bodhicitta, who is a bodhisattva, which is an incredible blessing, but from a yogi who has the clear light realization, who is a Chakrasamvara practitioner. Even just being in front of this person, she receives blessings and is purified. Also, this person’s neighbors and the insects and people around this yogi receive blessings and are purified. Being in front of Rinpoche is incredible. It is said that if this kind of practitioner crosses over a bridge, then under the bridge the insects, worms, and beings are liberated, their negative karma is purified. This is very fortunate.