Hare Krishna.
Pranams.
One stop-gap solution could be to disallow sending joining request temporarily.
Then, in the Description, just below askjoin button (which will not display once you have disabled it), just in the first line enter your email ID that will take the requests and manually add the new person to the google group.
Something Like:
Description
------------------------------
To JOIN GROUP:
We will revert back in 3 days time.
This group aims to understand, preserve and enrich Indian intellectual heritage. It is open to all scholars who value India's intellectual heritage and who study it in its various manifestations through primary sources.
------------------------
>> This could be the best use of bad bargain.