With the tractor jacked up and leaning substantially to the right and a new strainer part ready to screw in, I lost about 1.5 cups of hydro oil. There is really no way to plug the hole- it leaks from inside the suction fitting. And, of course, what does leak out is contaminated with metal filings, so it can't (shouldn't) be reused.
If you make the mistake of not cleaning this strainer while changing the fluid, you had better have the replacement part on hand or you WILL be doing another fluid change!!!!