Can I Undo InDesign's Automatic Superscript for trademarks?

Strictly speaking, you don’t have to worry that much about it. There is no legal requirement to acknowledge the marks of others, and for yours, you need to “sufficiently put the public on notice” that your marks are yours. This means stuff like the cover, some frontispiece that says “XYZ is a trademark of so-and-so”, once in a while in, for example, large type of a title of a chapter. Many writers pepper TM and R bugs everywhere and sweat if any are missed, but that’s a wasted exercise. And not that it matters, but in my work, my body copy uses the regular R and TM symbols that the typeface gives me, and it’s good enough. But that’s my personal preference.

I’m not aware that InDesign does automatically create a superscript glyph for the ™. In most fonts this glyph is designed as such. Can you look in the glyphs panel? Maybe you just need to choose another font that contains this glyph in normal size and position (it’s a little better in Cabrito Sans, Futura, Gill Sans Nova, Neue Helvetica, Neue Kabel, Real Text Pro, Rival Sans, Tosia, for example, and it’s quite normal in size and position in Adagio).

Yes, I think this is a matter of choosing a different font. Alternatively, you could apply a grep style to make the character larger and lower the baseline shift!