Toggle Class (classList Approach)

test.css

/*to show the image*/
.SelectedBorderOrgType .markIcon {
  display: block;
}
/*to hide the image*/
.NonSelectedBorderOrgType .markIcon {
  display: none;
}
.SelectedBorderOrgType .pillLabel1 {
  font-weight: 600;
}
.NonSelectedBorderOrgType{
  font-weight : normal;
}

test.html

<div class="NonSelectedBorderOrgType" onclick={toggleOrgType}>
    <img class="markIcon" src={markIcon} alt='marked'>
    <div class="pillLabel1">{type.LKUP_DSC__c}</div>
</div>

test.js

toggleOrgType(event){
const evt = event.currentTarget;
evt.classList.toggle('SelectedBorderOrgType');
evt.classList.toggle('NonSelectedBorderOrgType');
}