Is This A Cut Square From An Bavarian Stationary Envelope?

I don't believe so.

The Kreuzer values of this design can be found in two varieties -- (1) values in all four corners, and (2) values in the lower corners with posthorns in the upper corners. Those with values in all four corners are the earlier issues, and can be found on wrappers, postcards, and as individual stamps. In the wrapper and postcard formats, however, they are only found in 1 Kr, 2 Kr, and 2/2 Kr values. Thus, they are likely the imperf stamps. There are several possibilities. Does it have a watermark, and if so, what does it look like?

It appears to be a 3 Kruezer stamp from 1867. The red silk thread would suggest that.

Ah yes, the thread. Has to be MiNr 15 from 1867. Cat value €3 used.

Thanks for the answer, PostmasterGS and 1847bill!

But wait, there's more! In Michel-Spezial, numeral cancel "303" is in the second tier of scarce postmarks; in 1997, that category was an extra DM25 to DM60, and yours is nearly a perfect strike, so you might add another $10 to the valuation.

The ultra-rarities for Bavaria (Bayern in German) are #35, 894, 899, and 905-920.