Do gravitational waves affect time?

Yes, it has an effect on time. That's how we detected it. They are ripples in "spacetime", which you can think of as compressing space without affecting the speed of light. That's how LIGO works: it compares the time that it takes for a beam of light to travel. read more

Note that the Wikipedia definition of "gravitational wave effects" (General relativity ) does not mention time effect directly. Gravity is described by General Relativity as a tensor wave (not a scalar) in the geometry of Minkowki spacetime. read more

Yes, since gravitational waves are changes in the spacetime metric, they cause an observer to report that far observers experience time differently. However, the effects of observers on Earth is extremely small. Consider a simple binary system. As the objects orbit each other, they emit gravitational waves. read more