How do I remove a tool in the backpack without error?

If you just want to empty the backpack, you can do

backpack:ClearAllChildren()

But if you want to remove a specific tool only if it exists, use FindFirstChild() and check if it returns nil

local tool = backpack:FindFirstChild("Tool1")
if tool then
    tool:Destroy()
end

And for multiple tools:

local tools = {"Tool1", "Tool2", "Tool3"}
for i,v in pairs(tools) do
    local tool = backpack:FindFirstChild(v)
    if tool then
        tool:Destroy()
    end
end

If you're asking to effectuate the code you've written, and if it errors keep going in the script, you may want to wrap your code in a pcall(). This will make a protected call which, when the script errors it will let it continue.

local player = game:GetService("Players").LocalPlayer
local bp = player:findFirstChild("Backpack")

script.Parent.MouseButton1Click:connect(function() 
    pcall(function() -- this will make an anonymous pcall function
        bp.Tool:Destroy()
        bp.Tool2:Destroy()
        bp.Tool3:Destroy()
        bp.Tool4:Destroy()
    end)
    --script continuation...
end)