Drain the tofu and give it a few good squeezes between your hands to get the water out. Grate the tofu with the large holes of a box grater.
Heat the oil in a large non-stick pan over medium-high heat. Add the tofu and fry, stirring from time to time, until crispy and browned - about 4 to 5 minutes.
Place the chickpeas in a large bowl and smash them into a chunky paste. I squeeze them with my hands but a fork or potato masher also works.
Finely dice the tomato, celery and onion. Peel and grate the carrot. Add the vegetables and fried shredded tofu to the bowl with the chickpeas.
Dress with mayonnaise, dill, salt and pepper and mix well.
Place about a cup of shredded lettuce down each tortilla wrap. Top with the tofu-chickpea mixture. Fold in the short sides of the wrap, then roll the wrap up from the bottom over the filling.
Optional: toast the wrap in a dry pan to seal it shut and give it a crispy outside.