This error comes when you use chrome.storage.sync.set...to set the data greater than 8,192 bytes for a single item as chrome.storage.sync.set allows 8,192 QUOTA_BYTES_PER_ITEM.
Use chrome.storage.local.set, to save the large data...instead of chrome.storage.sync.set.
As chrome.storage.local.set can contains 5242880 :QUOTA_BYTES.
See https://developer.chrome.com/extensions/storage
Also, you can get the alert if still want to use chrome.storage.sync.set using below code:
chrome.storage.sync.set(function() {  
   var error = chrome.runtime.lastError;  
   if (error) {  
      alert(error);  
   }  
});   
If you are getting same warning with chrome.storage.local too, then
Reason: The data you are trying to store is greater than the allowed storage with local i.e. 5242880 QUOTA_BYTES.
Solution: You can set the permission as unlimitedStorage in manifest.json file.
  "permissions": [   
    .....  
    "unlimitedStorage",  
    .....  
   ],
For more regarding permission
1) https://developer.chrome.com/extensions/storage#property-managed
2) https://developer.chrome.com/extensions/permission_warnings#nowarning