Currently, you can only accept payments via credit card when accepting payments via Hurdlr’s payment collection feature.
If you accept payments other ways, you can certainly continue accepting them that way outside of Hurdlr’s payment collection feature. When sending the invoice, you would just be sure to disable the Credit Card payment processing option and keep the Cash/Check option selected.
Once your client makes the payment, go into the invoice and enter the cash payment and/or bank transaction deposit to link it to, so the status can be updated to Paid. You can follow the steps outlined here to do so.