Harvard’s outside scholarship policy is described at Types of Aid . Basically, if the student receives need-based grants from Harvard (“Harvard scholarship”), outside scholarships first replace the student work expectation ($3,500 at Harvard), then replace the need-based grants.
A student who receives a $40,000 outside scholarship and a need-based grant from Harvard that is $36,500 or more will benefit from only $3,500 of the $40,000 scholarship. A student who receives a need-based grant from Harvard that is under $36,500 will effectively lose the need-based grant, offsetting part of the benefit from the $40,000 scholarship.