public string GetContentType()

public async Task DeletingAttachments()
{
  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
    using (Table inspectionTable = geodatabase.OpenDataset<Table>("luCodeInspection"))
    {
      QueryFilter queryFilter = new QueryFilter { WhereClause = "ACTION = '1st Notice'" };

      using (RowCursor cursor = inspectionTable.Search(queryFilter, false))
      {
        while (cursor.MoveNext())
        {
          using (Row currentRow = cursor.Current)
          {
            IReadOnlyList<Attachment> rowAttachments = currentRow.GetAttachments(null, true);
            IEnumerable<Attachment> attachments = rowAttachments.Where(attachment => attachment.GetContentType().Equals("application/pdf"));

            IReadOnlyList<long> attachmentIDs = attachments.Select(attachment => attachment.GetAttachmentID()) as IReadOnlyList<long>;
            IReadOnlyDictionary<long, Exception> failures = currentRow.DeleteAttachments(attachmentIDs);

            if (failures.Count > 0)
            {
              //process errors
            }
          }
        }
      }
    }
  });
}