let value="test";
let myjsonobj = {
      "employeeid": "160915848",
      "firstName": "tet",
      "lastName": "test",
      "email": "test@email.com",
      "country": "Brasil",
      "currentIndustry": "aaaaaaaaaaaaa",
      "otherIndustry": "aaaaaaaaaaaaa",
      "currentOrganization": "test",
      "salary": "1234567"
}
Object.keys(myjsonobj).forEach(function(key){
  if (myjsonobj[key] === value) {
    delete myjsonobj[key];
  }
});
console.log(myjsonobj);