I was going to suggest the anti-drainback valve as well. If you still hear the noise with the new oil then try replacing the filter. I would be surprised if the Mobil 1 filter was the problem but it is worth trying since a new oil filter is a lot cheaper than a new engine or car which others are suggesting as possibilities. It may not make any different but I would be willing to gamble the cost of a new oil filter given the alternatives. Make sure to add some oil to make up for what is lost with the old filter.
Try the genuine Toyota filter or the Motorcraft filter if you can’t find the Toyota one easily.