Where the claim comes from
Screens do emit blue light, and blue light does affect the body's sleep timing at high enough exposure. The marketing takes that real fact and extends it to eye strain, which is a different question. Whether filtering blue light reduces the tired, dry feeling from screen work is an empirical matter, and it has been studied. The answer so far is not what the advertising implies.
It helps to separate the two claims, because they are not equally supported. The sleep-timing effect rests on light entering the eye in the hours before bed and shifting when the body expects to rest. The eye-strain effect rests on the assumption that visible blue light is itself what makes eyes ache after a long afternoon of work. Only one of those has held up under controlled comparison, and it is not the one printed on the box.
There is also a measurable difference between the light a screen throws and the light a summer sky throws. A monitor's blue output is a small fraction of what you get from simply stepping outside at noon. That gap matters when a product is marketed as though it were shielding you from something intense.