Are prayer beads (tasbih) an innovation?

The basis for the tasbih, or counting beads, is a hadith in which the Prophet ﷺ found a Mother of the Believers using date pits to count her glorification of Allah. The beads are a counting aid; the string simply holds them together.

Some object to the tasbih. This hadith is the basis for the counters: Saffiyah may Allah be pleased with her, the Mother of the Believers, narrated that the Messenger ﷺ came to her when she had in front of her four thousand date pits which she was using as counters for glorification of Allah. [Jami at-Tirmidhi 3554]

The counter is a way to keep count of one's litanies.