As pointed out, the problem was that the event handler was listening for any kind of click event in the window object. Instead I refactored the code and put the respective buttons in variables and added the addEventListener.
// contact-form opens upon clicking the "get a quote" Button
let quoteButton = document.getElementById('quote-button');
quoteButton.addEventListener('click', function() {
 let contactWrapper = document.getElementById('contact-wrapper');
  if (contactWrapper.style.display == 'none') {
    contactWrapper.style.display = 'flex';
  } else {
    (contactWrapper.style.display = 'none');
  }
});
//contact-form disapears when clicking "back" Button
let backbutton = document.getElementById('back-button');
backbutton.addEventListener('click', function() {
  let contactWrapper = document.getElementById('contact-wrapper');
    if (contactWrapper.style.display == 'flex') {
      contactWrapper.style.display = 'none';
    } 
});
solved pop up window does not open when code added in java script