Pride is inherent in the term Ownership therefore to me this phrase is grammatically incorrect
Am I correct in this? What is the rule of grammar that we are dealing with?
That's a tricky question because pride of ownership carries two meanings.
If pride of ownership means, having pride in one's possessions, then the term you are looking for would be something along the lines of (semantic) redundancy. Note, the definition of the word pride (n.) elation or satisfaction over one's own abilities, possessions, etc. Ownership, too, refers to possessions. So, here, we have the redundancy.
If, however, pride of ownership means, having pride (i.e., a sense of elation/satisfaction) in the knowledge that one owns something, it carries a different meaning.