One easy possibility is to use a UIWebView instead of a UITextView. The user isn't going to be able to edit the table anyway, so if the whole text view is not supposed to be editable, this is an easy choice.
If the text view is to be editable, then draw the table into an image context and include the image inline in the text view (iOS 7 only, because it gives you the full power of Text Kit). The table still won't be editable, because it is an image. But that shouldn't bother you, since your proposed labels wouldn't have been editable either.
I should also mention that if the text is all short (single words, essentially) and if you don't want to draw grid lines, you could just do it with tabs (another new iOS 7 feature).