No brush on a better bottle. I'd imagine it was included because the starter kit you ordered had a glass carboy option as well, and it would be logistically difficult to omit the brush for orders that select the plastic carboy option...so they just throw it in.
In a pinch, I've thrown a couple papertowels into the carboy filled with a gallon or so of PBW solution, and just swirled it to create agitation.
The much better option is to plan ahead, and use time, temperature, and concentration to clean your carboy for you. I have had some pretty ugly post-fermentation better bottles that I simply filled with a hot PBW solution, and left on the kitchen counter over night. I guarantee that by the next morning, the carboy will be spotless (and scratch free).