First, white marks usually mean that there's water in the finish - not in the wood. So the 1st thing is to make sure you removed all the finish.
To do that wipe the table down with a rag dipped in paint thinner. This will highlight areas where there's still finish. Use your stripper to remove this, or try a stronger stripper, one that has methyl(ene) chloride.
Once all finish is removed, you'll have to bleach out the ink marks. I'd start by wiping the stained area with laundry bleach (wear gloves and eye protection). Let it sit for 6 or more hours. If some stain is still there apply a 2nd or 3rd coat as needed. If you need to apply a 2nd coat, it's usually a good idea to apply the bleach to the entire surface. Once stain is out, wipe surface with a 50 -50 mix of water and white vinegar. Let dry for 24 hours, then LIGHT sand with a 220 grit paper. Remove dust (repeat sanding if needed), and then apply your stain and finish.
Let us know how you make out
Bob "Boardman" Borders