I was planning on using NSAttributedString to highlight portions of strings with the matching query of a user's search. However, I can't find an iOS equivalent of NSBackgroundColorAttributeName—there's no kCTBackgroundColorAttributeName. Does such a thing exist, similar to the way NSForegroundColorAttributeName becomes kCTForegroundColorAttributeName?
No, such an attribute doesn't exist in Core Text, you'll have to draw your own rectangles underneath the text to simulate it.
Basically, you'll have to figure out which rectangle(s) to fill for a given range in the string. If you do your layout with a CTFramesetter that produces a CTFrame, you need to get its lines and their origins using CTFrameGetLines and CTFrameGetLineOrigins.
Then iterate over the lines and use CTLineGetStringRange to find out which lines are part of the range you want to highlight. To get the rectangles to fill, use CTLineGetTypographicBounds (for the height) and CTLineGetOffsetForStringIndex (for the horizontal offset and width).