After electronic filing, Ohio school district form, SD-100 printed. What am I supposed to do with this copy of SD-100? Did TT not file a copy with the state?

 Usually  the School District return  is e-filed with the state return, but there are exceptions. Read the Ohio 'filing instructions" that TurboTax prepares, They will tell you if the SD100 was e-filed or if you have to mail it.

I see the explanation, but feel rather ripped off for the $25.99 plus tax I just paid to efile and still have to paper file.

It's more likely an Ohio Dept. of Taxation requirement than TT ripping you off. There was probably something unusual about your SD100. Part year resident of a district, for example.