Here I have added a node which subtracts a certain value from the mask. I am subtracting 0.5, because I happen to know that the grey used in the spots node is exactly a mid-grey (I chose it!) Subtracting 0.5 from that makes it black, or zero. This gives zero specular highlight in the fully masked areas.

However, subtracting 0.5 also turns the white areas of the mask into a mid-grey. So in order to keep the same strength highlights I have doubled the Specular Value to 2.0, as shown.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)