It's a little complicated.
Firstly, press Ctrl+Shift+I (Windows/Linux) or ⌘+⌥+I (Mac), and go to
Application tab (you might need to press the >> button). Click on Local Storage from left bar, and pick the discordapp.com result:
On the right bar, find "EmojiUsageHistory" Key, and copy the Value of it (right click on value, pick edit, copy it. As there's a lot of stuff in there, it might take some time)
As an example for this post, I'll remove the smirk_cat emoji (bottom row, fourth from right):
Paste the "EmojiUsageHistory" values you copied to your favorite text editor, and search for the emoji's name (or the snowflake, if it's a custom emoji. To find the snowflake of a custom emoji, write
\:name of emoji:, the number is the snowflake of emoji), should look like this:
Remove the parts until the next emoji, ensure that a
, is between the previous and the next emoji.
If you want to make sure that an emoji you want shows up on the list, find it and change
score to a high value (like 500).
Copy that text, edit the value of "EmojiUsageHistory" again and paste the values.
Restart discord by pressing Ctrl+R (Windows/Linux) or ⌘+R (Mac), the emoji will be gone from the list: