content_script.js

function updateTimeLogged() {
  var time = $("#log_hours").val() + "h " + $("#log_minutes").val() + "m";
  $('#log-work-time-logged').val(time);
}

$(document).on("change", "#log_hours", function(event) {
    updateTimeLogged();
});

$(document).on("change", "#log_minutes", function(event) {
    updateTimeLogged();
});


function isLogworkDialogOpen() {
   console.log("checking for #log-work-time-logged");
   return $('#log-work-time-logged').length === 1;
}

function hasFacelift() {
   console.log("checking if facelift has been applied...");
   return $("#log_hours").length === 1;
}

function checkDOMChange()
{

    if(isLogworkDialogOpen()) {
	
	console.log("Log Work Dialog is open!!");
	if(!hasFacelift()) {
            console.log("applying facelift...");
	    $('#log-work-time-logged').hide();
	    $('#log-work-time-logged').after('<input id="log_minutes" class="form.aui" type="number" min="0" max="45" width="10%" step="15" value="0"><p style="display: -webkit-inline-box;">&nbsp;min&nbsp;</p>');
	    $('#log-work-time-logged').after('<input id="log_hours" class="form.aui" type="number" min="0" max="8" width="10%" step="1" value="0"><p style="display: -webkit-inline-box;">&nbsp;hr&nbsp;</p>');
        } else {
	    console.log("already has facelift - nothing to do!");            
	}
    }

    // call the function again after 100 milliseconds
    setTimeout( checkDOMChange, 1000 );
}

console.log("start polling...");
checkDOMChange();

manifest.json

{
  "name": "Log Work Facelift",
  "version": "0.9.0",
  "description": "Make logging work great again!",
  "content_scripts": [
    { "matches": ["https://*.atlassian.net/*"],
      "js": ["jquery-3.1.1.min.js", "content_script.js"]
    }
  ],
  "manifest_version": 2
}