When to Use Articles Before Nouns
Nouns That Need Determiners: Countable Singular Nouns
We’ll start with some facts about nouns. First, some nouns in English can’t stand alone. For example, you can’t just say, “Cat crossed the road.” You have to say something like “A cat,” “The cat,” “Squiggly’s cat,” “Every cat,” or maybe “No cat.” “A,” “the,” the possessive noun “Squiggly’s,” “every,” and “no” are all examples of what linguists call determiners, and in English, some nouns have to have determiners.
So exactly which nouns need them? Countable, singular nouns, such as “cat,” must have a determiner.
Nouns That Don't Need Determiners: Proper Nouns
Of course, if you’re writing about a cat named Cat, or someone named Catherine who’s called Cat for short, then “Cat crossed the road” works. This brings us to one kind of noun that doesn't have to have a determiner: the proper noun. Proper nouns usually don’t have determiners; for example, you wouldn’t say “a Squiggly” or “every Squiggly,” except in the unusual situation where there’s more than one person named Squiggly.
Nouns That Don't Need Determiners: Plural Nouns
Plurals can go without determiners, too. Although you can say “the cats,” you can also just say “cats,” if you don’t have any particular cats in mind.
Nouns That Don't Need Determiners: Mass Nouns
Mass nouns—also called uncountable nouns—don’t need a determiner, either. Take the uncountable noun “information”: Although you can say, “I need your information,” or “I need the information,” you can also just say “I need information,” if you don’t want to be specific.
Mass nouns usually allow any determiner, provided it’s not one that implies the noun is countable. So you can’t say something like “one information,” “two information,” or “many information.” In particular, you can’t say “an information,” because “a,” which is a form of the word “one,” implies that “information” is a countable noun.
Nouns That Can Go Either Way
So what about the noun “time”? On the one hand, you can say “Knock three times,” and “Have a great time,” so “time” can be a countable noun—when it’s referring to particular events. On the other hand, “time” also has a general sense, as in “Time is on my side,” and “Marty McFly traveled through time.” Used this way, “time” is a mass noun. It sounds strange to say, “A time is on my side,” and “Marty McFly traveled through one time.”
In “Thank you for taking time to review my application,” we’re using “time” as a mass noun, so we can omit the “the.” Nevertheless, we can still use a determiner, as long as the determiner doesn’t imply countability. That means it’s also OK to say “the time.” To choose between “time” and “the time,” we need to say more about the definite article.
“The” is called the definite article because you use it when you’re talking about something that is distinguished from other things (in other words, something “defined,” or “definite”). If you say, “The cat crossed the road,” this cat might be distinguished from other things because it’s the only cat in the neighborhood, or just because it’s the only cat mentioned earlier in the conversation.
So if you write, “Thank you for taking the time to review my application,” that indicates you’re talking about a definite amount of time: whatever amount of time it takes to review your application. If, however, you just say, “Thank you for taking time to review my application,” you’re thanking the readers for any amount of time they might take to review your application, even if it’s just a millisecond. For that reason, “Thank you for taking the time” seems like the better option.
The argument isn’t airtight, though. You could argue that it will be obvious to your audience that you are thanking them for taking a sufficient amount of time to review your application; that only perverse, hostile readers would understand it as thanking them for taking any old amount of time; and therefore, it’s safe to leave out the “the.” All I can say at this point is that both options are used in the real world, and both are grammatically and stylistically defensible.