Tamago-su preparation
The way the recipe reads is: 


  Split open the membrane and dump the egg back in Vinegar &amp; mix well.


("Back" being the operative word there IE, "Dump it back into the vinegar") with the intent of consuming all parts of the egg, including the dissolved shell (the source of calcium), as reflected in the post-script to the recipe: 


  ...Egg Vinegar tonic to be an important source of strength and power. The
  protein, Calcium, Vitamins in the egg are well absorbed by our bodies.


The recipe also does not mention any additional vinegar after the 1 cup used at the beginning of the recipe.

So yes. Pour it back into the vinegar with the shell dissolved in it.

Just a note, make certain to wash your egg well before placing it into the vinegar &amp; keep in mind that from a food safety standpoint, you are consuming raw egg. You should probably try following food safety practices similar to those for home-made mayonnaise.