How would I make a script that checks if a player has things in their backpack?

There is a handy way to do this. As you said, GetChildren() is a built-in Roblox function that solves problems like these.

Put this in a LocalScript that's under ReplicatedFirst

local backpack = game:GetService("Players").LocalPlayer:WaitForChild("Backpack")
for name, child in pairs(backpack:GetChildren()) do
    if child:IsA("Tool") then
        if child.Name == "YourNameHere" then -- Replace YourNameHere with the name of the tool you wanna find
        print("Tool Found!")
    end
    end
end)

I hope this helps!