I think we need more information to answer.
Answer: The scenario fails to meet the definition of intellectual quotient because the intellectual quotient deals with human intelligence.
Explanation: This is because intellectual quotient deals with the test for reasoning abilities or human intelligences not emotions or speed of work. In the scenario there is no way the manager can measure her level of intelligence and for her to mark lack of intellectual quotient she must have subject the employee to certain reasoning test. Mary's patience is the test for her emotions and how she relate with people around her. Mary not been able to complete her task on time deals with her speed of work, that is, how fast she can perform her duties within the given time frame. Mary may be slow and impatience but that does not mean she lack intellectual quotient.
Homophones are words that sound the same but are different words.
Examples:
flour and flower
ate and eight
bare and beer
Her lack for compassion and her sense of horror I believe