Money in a bank account is "intangible" property and gifts of money are not subject to the US in situs rules. This article explains it best as I could find in a few minutes.
https://sommers-taxapedia.com/archives/summary-of-the-law-on-gifts-from-a-non-u-s-taxpayer/
A gift of stock, or real estate, could be subject to gift tax payable by your parent. But not cash.
