Remove a part only on clients screen (easy solution / fix) [?]

Use a RemoteFunction that tells the client that touched it to destroy it on their screen.

To do this, you should reference part.Parent and call GetPlayerFromCharacter from the part's parent. if GetPlayerFromCharacter returns a Player Object, then you can invoke the RemoteFunction with the first argument as the player, and the second argument as the part.

Now, in a localscript, you can handle the RemoteEvent.OnClientInvoke by checking if the PlayerObject name matches their's on the client. If it matches, then delete the part (second argument)

By the way, OnClientInvoke is not a signal. It requires a function.

RemoteEvent.OnClientInvoke = function(arguments_here)
end

ServerScript:

local ReplicatedStorage = game:GetService("ReplicatedStorage") -- This is just where I am going to store the remote event.

local players = game:GetService("Players")

local destroyEvent = Instance.new("RemoteEvent", ReplicatedStorage)
destroyEvent.Name = "destroyEvent"

local part = script.Parent

part.Touched:connect(function(hit)
    local hum = hit.Parent:FindFirstChild("Humanoid")
    if hum ~= nil then
        for _, v in pairs(players:GetPlayers()) do
            if v.Character = hit.Parent then
                destroyEvent:FireClient(v, part)
            end
        end
    end
end)

LocalScript:

local ReplicatedStorage = game:GetService("ReplicatedStorage")
local destroyEvent= replicatedStorage:WaitForChild("destroyEvent")

destroyEvent.OnClientEvent:connect(function(part)
    part:Destroy()
end)

Something like this should do the trick, hope this helped.