Sprinkle the shredded cucumber with salt and place it in a colander to drain for 10-15 minutes.
Stir together the yogurt, oil, garlic, salt, and vinegar in a bowl. Take the cucumber and squeeze out any more excess liquid using your hands or cheesecloth. Stir it into the mixture until well-incorporated. Finally, stir in the fresh dill. Season to taste and store cold.
For the savory grilled tofu:
Open the tofu, drain liquid from the package, and then wrap it in a clean towel, placing a heavy object on top of it to press out excess liquid from it. (Or use a tofu press). Let the tofu press for 10-15 minutes.
Preheat your grilling implement and make sure the grates are cleaned and well-seasoned with oil.
Mix together all of the ingredients for the tofu marinade until smooth. Cut the tofu width-wise into 8 approximately-equal slices. Use a baking dish or a large plate to pour the marinade over the tofu slices, then turn them over to coat both sides.
Grill the tofu pieces on an outside edge of the grill (don't use the hottest part; low-and-slow helps make the tofu a little chewier and crispier). Cook for 6-8 minutes per side, flipping halfway through. You want to see the tofu getting a little bit crisp on the outside with nice browning.
If desired, brush the tofu with a little bit more of the extra marinade after cooking.
For the grilled tofu gyros:
If desired, warm the pitas on the grill or however you prefer. Add two slices of tofu to each pita, along with plenty of lettuce, tomato, tzatziki, French fries if using, and any other toppings of choice. Enjoy hot.
Notes
Nutrition facts exclude French fries and assume only half of the sauce is used.