function who_remF (name, line, wildcards, styles)
 friendIS = wildcards[1]
 who_friends.friendIS = nil
 print(friendIS .. " has been removed from Friends List")
 who_win () -- redraws who list window with correct colors
end -- function who_remF

 who_friends [friendIS] = nil

Function used:
--------------
function who_remF (name, line, wildcards, styles)
 friendIS = wildcards[1]
 who_friends [friendIS] = nil
 print(friendIS .. " has been removed from Friends List")
 who_win () -- redraws who list window with correct colors
end -- function who_remF

LOG OF TESTS:
-------------
who test

1="Blake"
2="Chayston"

rem friend Blake

Blake has been removed from Friends List

who test

1="Blake"
2="Chayston"

rem friend 1

1 has been removed from Friends List

who test

1="Blake"
2="Chayston"

add friend Nick

Nick has been added to Friends List

who test

1="Blake"
2="Chayston"
3="Nick"

rem friend Nick

Nick has been removed from Friends List

who test

1="Blake"
2="Chayston"
3="Nick"

rem friend "Nick"

"Nick" has been removed from Friends List

who test

1="Blake"
2="Chayston"
3="Nick"

In the OnPluginSaveState () function..

 SetVariable ("who_friends", serialize.save ("who_friends"))
 SetVariable ("who_enemy", serialize.save ("who_enemy"))

and in the OnPluginInstall () function..

 require "serialize"
 who_friends = {}
 assert (loadstring (GetVariable ("who_friends") or "")) ()
 who_enemy = {}
 assert (loadstring (GetVariable ("who_enemy") or "")) ()

First tip I got was...
 for pos, val in ipairs(t) do if val == friendIS then table.remove(t, pos) break end end

Then another person jumped in and said...
in the future, consider using a map, where you insert with t[friendIS] = true 
and remove with t[friendIS] = nil, and iterate with pairs() instead of ipairs() 
(but the iteration is unordered)

  require "pairsbykeys"
  
  for k, v in pairsByKeys (who_friends) do
    print (k)
  end -- for

require "pairsbykeys"

who_friends = { }

function addFriend (who)
  who_friends [who] = true
end -- addFriend 

function removeFriend (who)
  who_friends [who] = nil
end -- removeFriend 

function showFriends ()
  
  for k, v in pairsByKeys (who_friends) do
    print (k)
  end -- for
end -- showFriends 

-- test

print (string.rep ("-", 40))

addFriend ("Nick")
addFriend ("Blake")
addFriend ("Chayston")

showFriends  ()

removeFriend ("Blake")

print (string.rep ("-", 40))

showFriends  ()

----------------------------------------
Blake
Chayston
Nick
----------------------------------------
Chayston
Nick

function has_key (wList, wName)
 for k, v in pairsByKeys (wList) do
  if k == wName then
   print("did it work?")
   return true
  end -- k
 end -- for
 return false
end -- has_key

function has_key (wList, wName)
  return wList [wName] ~= nil
end -- has_key

if who_friends ["Nick"] then
  print "Nick is a friend"
end -- if

function addFriend (who)
  who_friends [string.lower (who)] = who
end -- addFriend 

function has_key (wList, wName)
  return wList [string.lower (wName)] ~= nil
end -- has_key

whoNa = string.match(whoT, "( %a+)$")
if who_friends[whoNa] then

and

if has_key(who_friends, whoNa) then

neither seemed to work.

also changed to what you had except with ~= since != errors out

  if inv ~= nil then
   local y = 0
   for i, styles in ipairs (inv) do
     local x = 5
     for _, style in ipairs (styles) do
	  whoT = string.match (style.text, "^(.- %] %a+)")
	  if whoT == nil then
	   whoT = string.match(style.text, ".*")
	   if whoT == string.match(whoT, "^(.*Total.*)") then
	    x = x + WindowText (who_wind, "fontfour", whoT, 25, y + 1, 0, 0, colourGold)
	   end -- whoT double check
	  else
	   whoRa = string.match(whoT, "^(%a+ .-)")
	   whoCl = string.match(whoT, "^.-(%[.*%])")
	   whoNa = string.match(whoT, "( %a+)$")
	   if who_friends[whoNa] then
	    x = x + WindowText (who_wind, "fontfour", whoNa, x, y + 15, 0, 0, ColourNameToRGB("dodgerblue"))
	   elseif has_key(who_enemy, whoNa) then
	    x = x + WindowText (who_wind, "fontfour", whoNa, x, y + 15, 0, 0, ColourNameToRGB("red"))
	   else
	    x = x + WindowText (who_wind, "fontfour", whoNa, x, y + 15, 0, 0, style.textcolour)
	   end -- who_friends
	   if whoCl == nil then
            -- if class is a colored name, it doesnt capture it, figure some fix for it here
	   else
	    WindowText (who_wind, "fontfour", whoCl, 80, y + 15, 0, 0, style.textcolour)
	   end -- whoCl
	  end -- whoT
     end -- for
     y = y + font_height
   end -- for each who list item
  else
   WindowText (who_wind, "fontfour", "Who List will show up here", 25, 1, 0, 0, colourGold)
  end -- inv

	   whoNa = string.match(whoT, "( %a+)$")