These events arise when the Content Indexing (CI) Service cannot access a folder that is configured in "Catalog" of folders. It can occur in any of these situations:
1) a configured folder no longer exists
2) the permissions to access the folder are not set properly
3) network problems preventing access to the folder on a network share.
A 4135 event will be generated for each problematic folder.
If MS Exchange is removed from a server, non-existent WEB folders will generate these events. You'll have to go to Internet Information Services (IIS) to remove these folders. Examples are: \\backoffice, M:<domain name>\Exchange\MBX, etc.
Be sure to restart "IIS Admin" service after deleting problematic WEB folders or they will reappear in the CI Catalogs and generate 4135 Events. If you move and forget to index other non-Exchange folders that are cataloged for indexing, you'll get these events. So check the SYSTEM catalog as well.
To delete the non-existent directory references in the CI, drill down in Computer Management tool to: Services and Applications\Indexing Service. At this point, you will see the "WEB and "SYSTEM" Catalogs, and possibly others. Then drill down in each catalog to inspect and delete folders that are raising this event. A good reference on this is MS article ME308202