For example if in answer to the question, "what time does the shop close?" a tourist information officer might say, "I'll check on that for you."
Why wouldn't they say, "I'll check that for you."?
Learn English – the difference between “check something” and “check on something”
phrasal-verbsusage
Best Answer
Check means to examine (something) in order to determine its accuracy, quality, or condition. Check on is a phrasal verb that means verify, ascertain, or monitor the state or condition of.
It's a subtle difference between the two, and, in the example you gave, I think either could be applied.
If you asked me which one was more correct, I think I'd vote for check, rather than check on, but that was only after consulting a dictionary. Most tourist officers aren't that careful with their words before checking up on the hours of a village shop.
Oh, check up on means investigate in order to establish the truth about or accuracy of, which is, I suppose, another way of saying (nearly) the same thing.
Ref: these definitions were taken from NOAD