'>' or '==' not functioning properly?

Look at it logically:

--[[
== Equal to
~= Not equal to

< Less Than
> More than

<= Less than OR equal to
>= More than OR equal to
]]

--So, line 05, you're asking if the Credit Value (let's say it's 100) if More than 99.

--You could also say

if credits >= 100 then -- etc
  -- Ch-Ching!
else
 -- Not bought
end

Try this, the If Then statement is still running after it removes the cash and gives you the foil knife, you want to avoid that.

shop.KnifeFrame.MainFrame.Buttons.Buy1.MouseButton1Click:connect(function(onClick)
    confirmframe.Visible = true
    confirmtext.Text = "Are you sure you want to buy 'Foil Knife' ?"
    confirmyes.MouseButton1Click:connect(function(buy)
    local running = true --Every time this is clicked, then running is set to true
        if player.Credits.Value > 99 and running == true then --If you don't have enough money, then the script will skip these lines of code and running will still be true.
            player.Credits.Value = player.Credits.Value - 100
            purchasedprompt.Visible = true
            purchasedtext.Text = "You have brought 'Foil Knife' for 100 Credits"
            confirmframe.Visible = false
            running = false --How can both conditions in the next statement be true if this is false now.
        elseif player.Credits.Value < 100 and running == true then --If it took your money, then it shouldn't run. If you didn't have enough money, then running should remain true and will give you a warning.
            purchasedprompt.Visible = true
            purchasedtext.Text = "You don't have enough credits to buy"
            confirmframe.Visible = false
            running = false
        end
    end)
end)