The braided ring woven from the head's own skin at the pudi's circumference. The baddhi straps lace through it, so all the tension the head carries passes via the gajra — it is the structural anchor of the whole system.
It also matters in tuning: hammer taps on the gajra (downward to raise pitch, upward from below to lower it) are the fine adjustment between strap work and gatta moves. A gajra pulling unevenly shows up as a head that will not tune true around its circle.