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The Mercruiser trim pumps are typically self bleeding unless there is a large amount of air in the trim system (ie: empty trim cylinders, even then, the pump will bleed itself most of the time).
Have you checked your trimp pump reservoir to see if you have enough fluid it? If the fluid is low, add fluid as needed and run the trim pump up and down several times to purge out any air (the trim reservoir should be filled to the proper level with the drive unit in the down position, if the reservoir is almost empty and the drive is stuck in the up position, add enough fluid to lower the drive before filling the reservoir all the way to the fill line). The strange part is... pulling the drive unit should have had no effect on the trim fluid (unless for some reason you removed the trim hoses or if the fluid level was very low to begin with).
If you do need to bleed the trim system, below are the trim system bleeding procedures (but I really dont think you will need them)....
If for some reason the trim is sticking in the up position and your trim fluid level is ok, you may need to press down on the drive unit as someone presses the trim down button.
I hope that you find this information useful, thanks again for your question.