You might notice your offer letter says the externship is unpaid but you thought it came with a stipend. There is a difference between the two!
A paid opportunity implies that you are compensated for your services. A stipend implies that you are provided funds to cover the costs you incur during the program.
So, after the completing the externship projects, you are not paid for your services (remember, you are not working directly for your host company, nor Extern). Rather, your stipend is meant to cover any and all costs in connection with educationally related activities undertaken by the student within the externship.