Well, the title is a little misleading, because both "time of day" and "time of the day" are possible and can have the same meaning.[here] But "time of day" is more commonly used (when we're not mentioning a particular day, of course):
So you're more likely to hear:
We love to eat around this time of day.
But after we substitute "hour" for "time", the article is almost always in there:
So the previous example would become:
We love to eat around this hour of the day.
I imagine that native speakers of English would agree that it sounds a little off (or at least less natural) to say: ?We love to eat around this hour of day.
These 2-grams† bellow will show that the tendency to omit the definite article after time of exists in other similar phrases too:
- Month of the year is used with the, whereas time of year is more commonly used without.
- Day of month is comparatively rare, but time of month can be acceptable.
† or bigrams, or n-grams, if you will
To complicate things further, take a look at this 2-gram, which tells you that any time of the day is a little more common than any time of day; i.e., adding any kinda swaps the results around!
I guess this is because you're more likely to talk about a nonspecific time of a specific day, than to talk about any time of any day, for there is not much to say about it; hence the definite article before day.