the word 'plaid' means blanket. If you look up 'plaid' in the dictionary on www.learngaelic.net it's spelled 'plaide' - and pronounced 'plodge-yeh'
Maybe the non Gaelic speaking britons adopted the word from the Gaelic and started pronouncing it plad, or played, or pled. Not all of of the population of Scotland were always Gaelic speakers and some never were. Many words were borrowed on both sides of the fence