You may allow Groups.io members to sponsor your group in order to offset costs. 

On the Settings page, in the General panel at the bottom, select the box for Allow Sponsorships and Update Group: 

This will put a green button on the group's home page that says "Sponsor This Group":

 

A credit/debit card or Paypal may be used and the minimum amount is $5.  The group will receive the full amount of the sponsorship toward future payments.  Any fees associated with the transaction are absorbed by Groups.io.  Groups.io will be able to use the funds for their needs immediately, so this is also a way to support the site, even if you have a free/basic group.  The funds will be stored in the group's account indefinitely, to be used if/when needed.  Sponsorship payments are non-refundable. 

A message will be sent to group owners with details of the transaction.  The sponsor will also get an email notification from Groups.io.  You can also add a Member Notice of type Group Sponsorship that would automatically be sent to the sponsor.  The sponsor can also check on their Billing page to verify the transaction.  They may also receive a notice from Paypal or it would show up on the their credit/debit account.

Group owners (or mods with the Billing permission) may check the balance available on the Upgrade/Billing page for each group.

 

The official Groups.io user documentation is in the Groups.io Help Center.