a) Would you mind telling me which TV series it was?
"...which TV series it was" is an indirect question.
On the inversion of indirect questions, from https://en.wikipedia.org/wiki/Content_clause
...different syntax is used in direct and indirect questions: direct
questions normally use subject-verb inversion, while indirect
questions do not.
In spoken conversation, even though not grammatically correct per above explanation, the pattern in (b) is commonly used, and can be thought of as one of the many grammatical exceptions native speakers use in colloquial speech.