First, replace all the \w (Matches any letter, digit or underscore) with \s (Matches any space, tab or newline character). I believe you don't won't letter in phone number. Second, you need to add a quantifier {0,4} to the end of your Regex, just like you already did in other positions of the Regex.

So the final Regex will be ^[\d]{0,1}[\s]{0,1}[(]{0,1}[\d]{3}[-)\s]{0,2}[\d]{3}[-\s]{0,1}[\d]{0,4}

Because your regex is nonsense.

1. No need for [] for single group ([\d]{0,1} can be just \d?
2. \w does not match spaces, just [a-z0-9] in general case
3. You match starting ( but ending ) can be followed by - or any \w

function telephoneCheck(str) {

  let reg = /^\d?\s?\(?[\d-]+\)?\s?\d+/;
  return reg.test(str);
  
}

console.log("function: " + telephoneCheck("1 (555) 555-5555"));

1. You need to replace \w with \s for whitespace
2. You need to escape parenthesis \( and \)
3. You need to change [-)\w]{0,2} to [-\)]{0,1}[\s]{0,1} unless you want the unorthodox 1 (555)-555-5555 to be true.
4. The final [\d] should be [\d]{4} since you want exactly 4 digits at the end.
5. You can replace the {0,1} with ? when evaluating a single character that is optional.
6. You don't need brackets around single characters.

Here's the resulting code:

function telephoneCheck(str) {

  let reg = /^\d?\s?\(?\d{3}[-\)]{0,1}\s?\d{3}[-\s]?\d{4}/;
  return reg.test(str);
  
}

console.log(telephoneCheck("1 (555)555-5555")); // true
console.log(telephoneCheck("1 (555)5555555"));  // true
console.log(telephoneCheck("(555)555-5555")); //true
console.log(telephoneCheck("15555555555")); //true
console.log(telephoneCheck("1 (555)555- 5555")); // false
console.log(telephoneCheck("1 (555)-555-5555")); // false