As you are covered by US tax laws, you must report the gifts as required by law no matter who the recipient is.
If you give gifts of more than $17,000 per person per year, you are required to file form 709 to report the gifts. Actual payment of gift tax is not owed unless your total lifetime gifts are more than $13 million, but form 709 is used so the IRS can keep track of large gifts against your lifetime total. (Form 709 is not included in Turbotax, you will have to do it yourself. The deadline for reporting 2023 gifts is the same as the income tax deadline, April 15, 2024.) But that still means you can give your parents $17,000 each or $34,000 per year without triggering the reporting requirement.
(Whether they have a tax requirement for receiving a gift depends on the laws of the country where they live.)
You are covered by this requirement whether you transfer the money directly from a US bank account or from a foreign bank account that you control. It's still "your money" until the transaction is complete and you have given it to them.
I don't think it makes a difference what they use the money for, whether you are supporting their household or they use it to buy fancy cars, I think it's still a gift from you to them.
Lastly, if you own or control a foreign bank account that has more than $10,000 (US or US equivalent) at any time during the year, you are required to report this to the IRS on a report called the FBAR. No tax is owed, it is only a reporting requirement, and this one can be done online. The deadline for 2023 reports is April 15, 2024. https://www.irs.gov/businesses/small-businesses-self-employed/report-of-foreign-bank-and-financial-a...
