How to check if a player has a certain tool?

So, you would need to access the players' backpack, which will be easy since this is a LocalScript.

wait(2)
local plr = game.Players.LocalPlayer
local mouse = plr:GetMouse()
local char = plr.Character
local x = script:FindFirstChild("Wood")

local GetWood = true

function ShowProgress(tree)
	if tree == 'SmallTree1' then
		for i = 0,1,.01 do
			WC.BG.Progress.Size = UDim2.new(i,0,1,0)
			wait()
		end
		elseif tree == 'MediumTree' then
			for i = 0,1,.005 do
			WC.BG.Progress.Size = UDim2.new(i,0,1,0)
			wait()
		end
	end
end

mouse.Button1Down:connect(function()
	if game.Players.localPlayer.Backpack:FindFirstChild("Axe")
		if mouse.Target ~= nil and mouse.Target.Parent.Name == 'SmallTree1' and GetWood == true then
			local Wood = mouse.Target       
			if (Wood.position - char.UpperTorso.position).magnitude < 10 then
				GetWood = false
				WC = plr.PlayerGui.WoodChopper
				WC.BG.Visible = true
				ShowProgress('SmallTree1')
					for i,v in pairs(Wood.Parent.Leaves:GetChildren()) do
						if v:IsA('Part') then
						v.Anchored = false
					end
				end
				for i,l in pairs(Wood.Parent.Logs:GetChildren()) do
					if l:IsA('Part') then
						l.Anchored = false
					end
				end
				Wood:Destroy()
				WC.BG.Visible = false
				GetWood = true
			end
		end
	end                                                                  
end)

NOTE: I DID NOT FIX/CHANGE ANYTHING WITH THE SCRIPT OTHER THAN ADD THE TOOL FINDER.