Received scores of 8,8,7,6
Retake or apply without scores for test optional schools?
The 8s and 7 are above average and it really depends on the average test score of the schools your child is applying to for the Fall. In general, those scores are strong. What else does you child have in their application to show academic and social strength? Are they coming from a strong school program with a good track record to this independent school. What grade are they applying for - is that an entry grade into this school or a later grade only admitting on attrition? If you child retakes, what is the plan to raise those scores and do the schools require all scores or just the one you submit?
I would be inclined to submit - but not enough information from you and the to make a clear decision.