Show gui to player not working?

First it should be said that you have no reason to continuously use script.Parent when you already have a variable for it.

Anyways, your problem is line 09.

On line 8, you use a rather clever way to make the frame visible or invisible based on the TeamColor, but then you just go ahead and make it visible on line 09, making line 8 useless!

You could simply take out line 9;

--Tab your code correctly!
local function Check()
	Frame.Visible = Player.TeamColor == TeamColor
	Frame:TweenPosition(UDim2.new(0.15, 0, 0.15, 0), "Out", "Bounce", 1)
	wait(4)
	Frame:TweenPosition(UDim2.new(0.15, 0, -0.7, 0), "Out", "Bounce", 1)
	wait(2)
	Frame.Visible = false
end 

But then you're tweening the GUI no matter what -- Not exactly super efficient. You could do this;

local function Check()
	if Player.TeamColor == TeamColor then
		Frame.Visible = true
		Frame:TweenPosition(UDim2.new(0.15, 0, 0.15, 0), "Out", "Bounce", 1)
		wait(4)
		Frame:TweenPosition(UDim2.new(0.15, 0, -0.7, 0), "Out", "Bounce", 1)
		wait(2)
		Frame.Visible = false
	end
end 

Or if you only want the GUI to show when they FIRST join the team, and not when they respawn or anything, you can use the built in parameter of Changed events (it's equal to the property that fired the event);

local function Check(property)
	if property == "TeamColor" and Player.TeamColor == TeamColor then
		Frame.Visible = true
		Frame:TweenPosition(UDim2.new(0.15, 0, 0.15, 0), "Out", "Bounce", 1)
		wait(4)
		Frame:TweenPosition(UDim2.new(0.15, 0, -0.7, 0), "Out", "Bounce", 1)
		wait(2)
		Frame.Visible = false
	end
end