Looking on the internet deeply has found these results:

Thanks for your understanding is the most popular phrase on the web.

Thanks for understanding 1471,000 results on the web	Thanks for your understanding 1799,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Great. Well, thanks for understanding. Thanks, D., thanks for understanding. Not every guy would be cool with that, so thanks for understanding. So, again, thanks for understanding.	Thank you for your understanding and I will ensure that it never happens again. In the name of these poor children, we thank you for your understanding. I would like to thank you for your understanding. Thank you for your understanding, Mr Dimitrakopoulos. Mr President, thank you for your understanding. Mr President, Vice I do, though, thank you for your understanding, Mr President. Nevertheless, I thank you for your understanding.

Thanks for understanding

1471,000 results on the web

Thanks for your understanding

1799,000 results on the web

More popular!

Thank you for your understanding and I will ensure that it never happens again.
In the name of these poor children, we thank you for your understanding.
I would like to thank you for your understanding.
Thank you for your understanding, Mr Dimitrakopoulos.
Mr President, thank you for your understanding.
Mr President, Vice
I do, though, thank you for your understanding, Mr President.
Nevertheless, I thank you for your understanding.