How do I do a Check?

In your if statement you can look to see if the tool is in the backpack or the StarterGearby doing this:

if not Player.Backpack:FindFirstChild("OCA Nano") and not Player.StarterGear:FindFirstChild("OCA Nano") then

I used and not which means if that statement is false(In this case it would mean if it's not in the backpack or startergear). I also used FindFirstChild which looks for a child in Startergear and the backpack. So that's how you do a quick check. Just check if the tool is in BackPack or startergear

Your final code should look like this.

local Part = script.Parent --Part to get touched
local Tool = game.ReplicatedStorage["OCA Nano"] --The tool you want to give them
local TeamColor = "Bright blue" --Team color here

Part.Touched:connect(function(hit)
    local Player = game.Players:GetPlayerFromCharacter(hit.Parent)
    if Player and Player.TeamColor == BrickColor.new(TeamColor) and  not Player.Backpack:FindFirstChild("OCA Nano") and not Player.StarterGear:FindFirstChild("OCA Nano") then
        Tool:Clone().Parent = Player.Backpack
        Tool:Clone().Parent = Player.StarterGear
    end
end)