I am going to presume that when you mean "text-only brochure" you mean "8.5 x 11 monochrome laserjet." I won't get into a critique of the logo itself.
With some leeway for size and production considerations, a logo is basically meant to be unalterable: it must be used like a badge without amendment.
However, the designer (you) is tasked with coming up with a few alternates for specific purposes, and typically, this means a full one, an approved reduced-content version for specific use-cases (like those corporate sponsor logo banners), and then 1-color, 2-color, 4-color, and RGB versions of those.
You will also want to have a version that does not require a 100% black flood fill on the whole piece or force all your collateral to have a black banner to accommodate the logo mark.
So the "easy" way for the image posted is to invert all colors, then desaturate all colors, then adjust the contrast/levels to produce a black and white version. Obviously this would be done differently and more appropriately with the original illustrator file. For AI, just "make all the black, white; then make all the colors black"
For a 1-color version, you probably want to eliminate the neon-glow effect, and reconsider the gradient. For printed items, you can have quality issues with fine dot patterns: sometimes "dot gain" floods the gaps and causes a splotchy appearance or screws up the contrast. Also, tight gradients may not print well on a t-shirt.
Note that a true greyscale (not rgb or cmyk) is really a brightness map, and is suitable for 1-color printing whether that color is black or some other ink.
Below is the result of (in Photoshop): ctrl+I,ctrl+U (desaturate fully),ctrl+L (levels adjust the darks to black and the lights to white).