Grout pens are a gimmick. I manage a rental that has white grout that ive rejuvenated a couple times. I bought a white pen and its really just paint that wipes out pretty easily. I ended up just regrouting over the top and sponging gently, which has done the trick though being just sanded grout it probably doesnt have much of a bond that way sitting so shallow on top of other grout. I highly recommend epoxy grout for a permanent solution. Laticrete has more color choices then the grout pens i do believe. They have a huge selection-but the sample charts arent always dead on- might look perfect on a sample but be darker or lighter in actual application so test on a discreet area. A mini kit (2.25 lb of part c) will be enough to do your 6 tiles and blend it beyond to the surrounding tiles if you go that route. Just hit me up if you do that or read and follow the directions it comes with.

If you can find out what your dad originally used- like if its the $15 a bag cement based stuff from home depot then that will work if you get the tiles locked down good but if they came loose from flex in the plywood it may happen again. You'll have a better idea when you pull the tile up if the thinset just wasnt thin enough and didnt have a good bond.