There are places where we write to people whose opinions matter greatly to us because they’re responsible for making decisions on promotions, so their impressions of us are important.
Did I use the words "they’re," "there," and "their" correctly?
If you are uncertain, let us go through some simple rules to know which word to use where and when.
"They’re" is a contraction of the words "they are." It is never the correct word to use when saying "they are" would not replace it, and neither of the other words is ever the correct word to use when "they are" would replace it. It is that simple.
"There" is a place. It may also be a point in time, but often "then" might be a better word to refer to a point in time. However, not always. For example, we would say "there was a time" when referring to the place in time. "It happened then" would refer to a point in time whereas "it happened there" would refer to the place it happened. It will never refer to people, especially regarding ownership. It will always be a place or a time, and, most generally, a place.
"Their" refers to ownership by other people. It used to be a plural possessive. However, with "they" and "them" being acceptable pronouns for individuals, it now denotes ownership by someone else or others. Simply, "their" denotes ownership.
So, let’s review the opening sentence to determine if it was written correctly.
It opened with "there" referring to a place. "There" was the correct word.
About halfway through it contained "they’re." We could have replace "they’re responsible" with "they are responsible" without changing what was meant. "They’re" was the correct word.
Toward the end of the sentence the word "their" was used in conjunction with "impressions." For it to be correct, we must be referring to the ownership of "impressions." We were writing to "people," and those people do, indeed, own or possess their impressions of us. "Their" was the correct word.
Their you go . . . I mean, there you go, of course, with "there" being the place you will find the rules!