I'm about to tell you, but be very careful in deciding you want to do this, or at least save a copy of the original.
Those greater than signs, provided you have not cut out the quote lines that occur before them, are what lets the reader know "who said what" in the context of a multi-person exchange and used to be the de facto standard in plain text email.
At the very least, if you know that a sequence of, say, four greater than signs refer to a message by Cindy, I'd be replacing ">>>>" with, "Cindy:" and that three greater than signs refer to a message by Bob, replacing ">>>" with, "Bob: ". There may be spaces between each greater than sign, too.
In any case, if you want to do a quick and dirty removal of every single greater than sign.
1. Get yourself to the very top of the document. CTRL+Home.
2. Hit ALT+H,R (Home Ribbon, Find and Replace option) to bring up the Find and Replace Dialog.
3. In the Find What (ALT+N) edit box, enter a greater than sign.
4. Leave the Replace With (ALT+I) edit box empty.
5. Activate the Replace All (ALT+A) button.
Every instance of greater than sign in the document will now be gone, just as if you had found each and back spaced it out.
Obviously, if you wanted to follow my advice, you'd enter ">>>>" in the Find What edit box and "Cindy: " in the Replace With edit box, etc., etc., etc.
There are also buttons for Replace (one occurrence, the one it finds first based on where your insertion point is positioned, ALT+R), Find Next (without replacing, ALT+F), and Cancel buttons. There is also a More button that allows you to set all sorts of additional formatting parameters, use wildcards, etc., the scope of which is beyond discussion here.
Brian - Windows 10, 64-Bit, Version 21H1, Build 19043
It is better to be hated for what you are than to be loved for what you are not.
~ André Gide