I live just outside of Toronto Canada, about a yea ago, my sister in
law gave my mother a blue holly plant for Christmas. She has been
growing it in the house since she received it. I had the opportunity
to take a look at the plant the other day, and it had spider-like
cobwebs on it, similar to the webs built by inchworms.

Any ideas how to get rid of this permanently without hurting the
plant?

It grows along some other plants, but only the holly has the weblike
problem.

Thanks