You don't say what fruit you're using, but I would interpret the recipe as meaning, press as much fruit as humanly possible through the strainer, so that all that's left is a little seedy residue (I'm clearly thinking raspberries or strawberries here...)--the point of the strainer being not so much to drain the fruit as to puree it. If you've got enough good stuff left in the strainer to raise the question about whether the recipe wants you to use it, I'm guessing you need to be a little more aggressive in forcing the fruit through the strainer (and more force would yield a thicker product to mix with the cream...)
