The Emergency Fund is the one item in EveryDollar that cannot be deleted due to how it is hardwired into EveryDollar.
Also, if a line has been turned into a Fund and labeled as "Emergency Fund" (spelled and capitalized just like that), then it can't be deleted individually either.
There is one workaround where if you delete the entire Savings group from the budget (which you can do when you sign into the desktop version of EveryDollar) then that will also delete the Emergency Fund.
If you do this, then any transactions that are tracked into the Savings Category will be moved back to the Transactions Queue. Then, when you re-create the Savings Category and put all of your Funds back in there, you can drag those back into the new Fund lines.