Grumio fears that Katharina's sharp tongue and fierce temper will make life unbearable for Petruchio and everyone around him. He worries about the constant arguments, quarrels, and disruptions that such a marriage would cause. He also expresses concern for Petruchio's well-being, fearing that Katharina's shrewish nature would wear him down and make him miserable.
However, Grumio's initial reservations gradually shift throughout the play as he witnesses Petruchio's skillful taming of Katharina. When Petruchio succeeds in subduing her temper and transforming her into a more obedient and gentle woman, Grumio's attitude changes from apprehension to admiration.
In the end, Grumio comes to see the positive outcomes of Petruchio's unconventional approach. He realizes that Petruchio's methods have brought peace and harmony to the household, and he ultimately acknowledges the success of Petruchio's strategy in taming the shrew.