Some articles on reinsertion, reinsertions:

R* Tree - Difference Between R*-trees and R-trees
... revised node split algorithm and the concept of forced reinsertion at node overflow ... Deletion and reinsertion of entries allows them to "find" a place in the tree that may be more appropriate than their original location ... In order to avoid an indefinite cascade of reinsertions caused by subsequent node overflow, the reinsertion routine may be called only once in each level of the tree when inserting any one new entry ...