As nobody seems interested in answering you, and you asked how to realize your request in javascript, in spite of having presented code in jQuery, here is a solution:
const MyTableBody = document.querySelector('#Table-3cols tbody')
  ,   BtRemC3     = document.querySelector('#Bt-Clean-col3')
BtRemC3.onclick=_=>
  {
  MyTableBody
    .querySelectorAll('td:nth-child(3)')
    .forEach(xTD=>
      {
      if (xTD.textContent==='')
        {
        let pTR = xTD.parentElement
        pTR.removeChild(xTD)
        pTR.cells[1].colSpan = 2
        }
      }
    )
  }
table { border-collapse: collapse; margin: 1em }
td { border: 1px solid grey;  padding: .6em 1em}
thead { font-weight: bold }
<button id="Bt-Clean-col3">Remove empty Cols 3</button>
<table id="Table-3cols">
  <thead>
    <tr> <td>col 1</td> <td>col 2</td> <td>col 3</td> </tr>
  </thead>
  <tbody>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td></td>   </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td></td>   </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
  </tbody>
</table>
 
 
explanations for:  (arrow functions)
BtRemC3.onclick=_=>
  {
  MyTableBody
    .querySelectorAll(`td:nth-child(3)`)
    .forEach(xTD=>
      {
this is like :
BtRemC3.addEventListener('click', function()
{
  MyTableBody.querySelectorAll('td:nth-child(3)').forEach( function(xTD)
  {
so, for the complete code this is :
const MyTableBody = document.querySelector('#Table-3cols tbody')
  ,   BtRemC3     =  document.querySelector('#Bt-Clean-col3')
  ;
  
BtRemC3.addEventListener('click', function()
{
  MyTableBody.querySelectorAll('td:nth-child(3)').forEach( function(xTD)
  {
    if (/@E/.test(xTD.textContent) ) // previously  (xTD.textContent==='')
    {
      let pTR = xTD.parentElement;
      pTR.removeChild(xTD);
      pTR.cells[1].colSpan = 2;
    }
  });
});
table { border-collapse: collapse; margin: 1em }
td { border: 1px solid grey;  padding: .6em 1em}
thead { font-weight: bold }
<button id="Bt-Clean-col3">Remove Cols 3 with '@E'</button>
<table id="Table-3cols">
  <thead>
    <tr> <td>col 1</td> <td>col 2</td> <td>col 3</td> </tr>
  </thead>
  <tbody>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>blah blah blah@E  blah </td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>blah blah@E  blah </td> </tr>
      <tr> <td>aa</td> <td>bb</td> <td>cc</td> </tr>
  </tbody>
</table>
 
 
I also changed the test about your @E value
regular expression to test if xTD.textContent contain '@E' 
please read How to check whether a string contains a substring in JavaScript?