You can't really avoid it, but here are some tips.
Rename your "global.css" to something like "jsdf754nd7.css" and embed it in your headerinclude template. Make sure to use the correct path.
<link rel="stylesheet" href="jsdf754nd7.css" type="text/css" >
Minify your stylesheets. This will make it harder, unless they use unminify tools. It'll also make the size of your css file lower.
I suggest a site like: http://csscompressor.com/
Pro tip: Recode the whole MyBB theme and use your own code. Means, stop using the MyBB tables and start using divs. I'm sure they'll give up on this, because it'll really take long to rip.