Hi George, 

Please check with the below code snippet.

To add the changes, you'll basically have to override the existing function by monkeypatching the code.

odoo.define('your_module.name', function (require){

    var publicWidget = require('web.public.widget');

    publicWidget.registry.subscribe.include({
        _onSubscribeClick: async function () {
            var self = this;
            var $email = this.$(".js_subscribe_email:visible");

            if ($email.length && !$email.val().match(/.+@.+/)) {
                this.$target.addClass('o_has_error').find('.form-control').addClass('is-invalid');
                return false;
            }
            this.$target.removeClass('o_has_error').find('.form-control').removeClass('is-invalid');
            let tokenObj = null;
            if (this._recaptcha) {
                tokenObj = await this._recaptcha.getToken('website_mass_mailing_subscribe');
                if (tokenObj.error) {
                    self.displayNotification({
                        type: 'danger',
                        title: _t("Error"),
                        message: tokenObj.error,
                        sticky: true,
                    });
                    return false;
                }
            }
            const params = {
                'list_id': this.$target.data('list-id'),
                'email': $email.length ? $email.val() : false,
            };
            if (this._recaptcha) {
                params['recaptcha_token_response'] = tokenObj.token;
            }
            this._rpc({
                route: '/website_mass_mailing/subscribe',
                params: params,
            }).then(function (result) {
                let toastType = result.toast_type;
                if (toastType === 'success') {
                    self.$(".js_subscribe_btn").addClass('d-none');
                    self.$(".js_subscribed_btn").removeClass('d-none');
                    self.$('input.js_subscribe_email').prop('disabled', !!result);
                    if (self.$popup.length) {
                        self.$popup.modal('hide');
                    }
                }
                // make the changes you need accordingly or comment out the below code.
                self.displayNotification({
                    type: toastType,
                    title: toastType === 'success' ? _t('Success') : _t('Error'),
                    message: result.toast_content,
                    sticky: true,
                });
            });
        },

    })

})

Regards