What is this black tape on my laptop's keyboard?
It could be

an ESD shield, to prevent electrostatic (dis)charge to/from fingers, and/or
an EMI shield to prevent RF radiation ingress or egress through the gaps between keys or through non-conductive keys, per FCC rules.

In that case, small rips are ok, but all of it must be conductively interconnected. Of course, best to replace the whole thing.