Well... did you expect it to work?
When you do BETWEEN two integer values, SQL will assume that you want an integer comparison, not a strign comparison (and the sort order is different, so it's important). As a result, it tries to be helpful, and convert the column values to integer - and of course it fails, because there is non-numeric data in teh table. You can try converting your vlaues to string, but you will have to fill them with leading zeros:
DELETE FROM TestId WHERE id BETWEEN '06' AND '10'