Someone well versed with tradition and rituals are best to give you a sloka you are seeking. So far that has not happened.
Reference to Gita is misplaced and hence I wanted to share this findings with you based on little research online.
If you ask for direction it is better to get right direction than wrong direction.
Gita is for mainly understanding. The citation and translation provided in this thread is from this website below
BG 2.40: Working in this state of consciousness, there is no loss or adverse result, and even a little effort … Commentary: The great danger we face is that we may not get the human form in the next life, and instead go into the lower species of life, such as animals, birds, …
While literal translation was supplied from this site, if you read the description and commentary it talks about something else unconnected to the issue you raised
For context you can look up the prior sloka
BG 2.39: Hitherto, I have explained to you Sānkhya Yog, or analytic knowledge regarding the nature of the soul. … Commentary: The word <em>Sānkhya</em> comes from the roots <em>Sāṅ</em>, meaning “complete,” and <em>khyā</em>, meaning “to know.” So <em>Sānkhya</em> means the …
The meaning as stated from that site is, Krishna explaining to Arjuna thus:
"Hitherto, I have explained to you Sānkhya Yog, or analytic knowledge regarding the nature of the soul. Now listen, O Parth, as I reveal Buddhi Yog, or the Yog of Intellect. When you work with such understanding, you will be freed from the bondage of karma."
I usually do not trust commentaries except from very few because I found lots of misinformation in the internet.
Therefore I checked the meaning of Gita 2.40 elsewhere also which makes more sense in the context of Gita verse 2.39. The website with commentaries is full of holes.
The summary meaning that I got was this (paraphrasing)
The verse begins amplification of Karma Yoga and how it protects one and there are no negative effects. Buddhi yoga is same as Karma yoga in this context. I checked Sankara's commentary translation also just to be sure,
Karma yoga is not Karma (like rituals or prayers) but attitude with which one does one's duties.
Clearly the verse 2.40 is not applicable to your question unless you want to study the topic of Karma yoga which is rather involved and non trivial.
Now coming to your question here are my laymen suggestions. Please stay in touch with your parents over the phone or video calls (like whatsapp calls).
Do your duties at home knowing that no person can do anything to change the Prarabdha Karma of another. So by prayer you cannot alter what happens to your parents but you will have mental strength to help them the best way.
If you can visit them do that when possible.
Surrender to God all your worries. You can choose to chant any verse that inspires you to surrender. Simple chanting of names of God is fine. Meditate and everything will be fine because by design everything is fine. Learn to accept life as is. Stop looking for any quick fixes like mantras
All the best