Whisk soy sauce, water, vinegar, brown sugar, ginger, garlic, and Worcestershire sauce together in a bowl and pour into a 1-gallon resealable plastic bag. Add chicken tenders, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for at least 1 hour, or up to 4 hours.
Preheat an outdoor grill for medium heat and lightly oil the grate.
Remove chicken from the marinade and shake off excess. Discard the remaining marinade.
Place chicken on the grill and cook until no longer pink in the center and the juices run clear, 3 to 4 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).