Is the concept of the 'inner child' considered to be pseudoscience?
I Google(-scholared) the term too and indeed I would classify it as pseudoscience.
The hits are mainly books, or dodgy journal papers. No hits that are pointing to the more established journals. While recognizing this doesn't prove that the concept of the inner child is bogus, or that it's not classified a science, it is a strong indicator that the concept has not (yet?) been embraced by scientists.
The term sounds to fit the idea of the 'pure, innocent, unblemished' beings children are supposed to be, not yet molded to fit society. I guess it's an interesting idea, but it sounds New Agie to me.
However, there are people way more proficient in Psychology hangin' around here, so a more authorative answer can likely be expected anytime soon.