There is a certain type of memes that contain the phrase "The guy she told you not to worry about". I am confused about the use of "she" on it, since the only person who tells you something is a guy. Is this proper English?
The answer that "that" is omitted,(the guy that she told you not...) is true however I might clarify why the "she"
I believe this is an example of a "woman to woman" conversation.
The context would be important. I can imagine this if a woman was going out on a date with a man who passed some limits on making unwanted sexual advances; that the woman that this happened to had felt comfortable accepting his invite because another women who knew him told her "he's a good guy" or vouched for him etc. A guy friend (assuming we're talking about a heterosexual date) would have no real experience about how he would act in private with a woman.
I believe it's pretty normal for a woman to ask another woman about whether it would a good idea to go out with someone. –
edit/addition @Hot Licks made a good comment that if used as a general expression, it doesn't need to refer to a particular incident, the "she" could be an unspecified third party ... he used the example "the guy your grandma warned you about".
Other posters are right that "she" is doing the telling, about "the guy". Essentially, the phrase means "she told you not to worry about some guy, and this is him." However, there is a specific "she" and a specific (kind of) "guy" implied in the meme.
The full meme is
You vs the guy she told/tells you not to worry about.
This is setting up a competition or comparison between "you" and "the guy (who she said not to worry about)". Key to this meme is in the pictures (Google image search here). They generally juxtapose a regular-looking guy with a much more attractive/younger/more muscular man.
One example compares "you": Curious George cartoon vs "the guy she tells you not to worry about": Harambe, an actual gorilla. Another compares a "pet rock" (a stone with googly eyes pasted on) with Dwayne "The Rock" Johnson, former professional wrestler and action movie star.
Here, "you" is used to address a hypothetical (male) person. The implication is that "she" is "your" girlfriend or wife. "He" is some guy she knows. "You" have felt threatened by him, but she says not to worry (he's just a friend).
The punchline of the meme is that really, you should worry, because he's much more attractive as a potential mate than you are, as illustrated by the images representing each of you.
This seems to be a zero-realisation of "that".
"The guy (that) she told you not to worry about"
The phrase "the guy she told you not to worry about" is an answer to the implied question, Who is that guy?
Let's call him Mark--"the guy" Let's call the woman Lola. Let's call the questioner, who asks "Who is that guy?", Steve.
Steve used to be going out with Lola. But now Lola is with Mark. And Steve asks his friend, or acquaintance, "Who is that guy?"
And his friend says: "The guy (Mark) she (Lola) told you (Steve) not to worry about. (Lola said to Steve, "Don't worry about Mark. He's just a friend."
The meme seems to be two photos, Steve (the guy who lost Lola) and Mark (the guy who took Lola away from Steve).
The friend could be female, but it's likely a conversation between two men--the friend and Steve--in a bar or similar place where they see Lola and Mark together.