Perhaps the Letter of Offer means your admission letter to the program. Receiving an admission letter doesn't mean you already have to accept your admission offer or pay for your tuition fees right away. You'll have to contact the scholarships department of the university about their awarding timeline (application deadline, application process, announcement of scholarship recipients, etc) so you can compare it with the deadline for accepting your place at the university.
Is the scholarship you're applying for related or sponsored by the university? If so, it's best to contact the university directly about this matte and look for the contact person in charge of the scholarships (maybe Scholarships Section/Division). If not, you'll have to contact both the university and the organization who grants the scholarship and try to coordinate with them.