The destroy route will take an id route parameter and delete the contact with that id from the database, using the mongoose .findByAndDelete() method:

// ./controllers/ContactController.js

// ...

module.exports = {
  async index(ctx) {
    const contacts = await Contact.find();
    ctx.body = {
      status: 'success',
      data: contacts
    };
  },

  async store(ctx) {
    const { body } = ctx.request;
    let contact = new Contact(body);
    contact = await contact.save();
    ctx.body = {
      status: 'success',
      data: contact
    };
  },

  async show(ctx) {
    const { id } = ctx.params;
    const contact = await Contact.findById(id);
    ctx.body = {
      status: 'success',
      data: contact
    };
  },
 
  async update(ctx) {
    const { id } = ctx.params;
    const { body } = ctx.request;
    await Contact.findByIdAndUpdate(id, body);
    const contact = await Contact.findById(id);
    ctx.body = {
      status: 'success',
      message: 'contact successfully updated',
      data: contact
    };
  },

  async destroy(ctx) {
    const { id } = ctx.params;
    await Contact.findByIdAndDelete(id);
    ctx.body = {
      status: 'success',
      message: 'contact successfully deleted'
    };
  }
};

We add the corresponding router definition, as follows:

// ./middleware/router.js
// ...

router
  .get('/', async ctx => (ctx.body = 'Welcome to the contacts API!'))
  .get('/contact', contactController.index)
  .post('/contact', contactController.store)
  .get('/contact/:id', contactController.show)
  .put('/contact/:id', contactController.update)
  .delete('/contact/:id', contactController.destroy);

// ...

Making a request to DELETE /contact/{contactId} with the specified id should return a response similar to the following:

{
    "status": "success",
    "message": "contact successfully deleted"
}