We have been discussing this. ["We" is the NBA Nemeth Code for Math and Science Committee.]
The Nemeth Code does not include a symbol specifically for the "tee" or "down tack" sign. So, it must be "represented by the use of one or more letters suggestive of the name of the shape being represented." We cannot use _% $t _: or even _% $d _:, because these are the Nemeth Code symbols for "triangle (equilaterial)" and "diamond," respectively.
For the "down tack" or "tee" sign, we might use _% $dt _: or perhaps _% $tee _: and, of course, we must identify the symbol and describe the print sign it represents in a transcriber's note or listing on a special symbols page (NC1972 §107).
So, I might transcribe "w with superscript ⊤" as _% w^$tee _: And, I might transcribe a longer expression, like "g(x)superscripted ⊤(Df)" as
_% g(x)^$tee"(,df) _:.
Thank you for asking (complete with a Wikipedia link). Braille on!