Your dog noses through gravel, then crunches on a stone. This is not a behavior to wait out while you practice "leave it." Rocks can break teeth or cause a dangerous blockage. If you think your dog swallowed one, contact your veterinarian promptly and tell them the likely size, material, and time. Vomiting, pain, lethargy, or loss of appetite after swallowing an object needs urgent veterinary attention. Do not induce vomiting unless a veterinarian tells you to.
Repeatedly eating non-food objects is sometimes called pica. It can have medical or behavioral causes, so arrange a veterinary evaluation rather than assuming your dog is bored. Your vet may ask about diet, digestive symptoms, and when the behavior began.
Keep the next walk safe
Avoid gravel-heavy routes and keep your dog on a secure lead where you can watch what they investigate. Clear accessible stones from a yard if practical and supervise outdoor time. A well-fitted basket muzzle may be part of an individual safety plan, but it must be introduced gradually and checked for fit, breathing, and drinking. It does not replace veterinary care or supervision.
Teach "leave it" with easy, harmless items at home: reward your dog for turning away before they take the item. Practice a separate fair trade for items already in the mouth. Don't chase, corner, or pry at a guarding dog's mouth. Once your vet has assessed the risk and you have a safe setup, move practice to a quiet outdoor area with no loose rocks within reach.
Training is worth doing, but prevention carries the load while the dog is still learning. A swallowed rock is not a lesson you need them to learn the hard way.
Sources: VCA Animal Hospitals: Pica in Dogs. Dogs Trust: Resource guarding in dogs.