Is it permissible to pay back a small debt by placing it among the owner’s money or in their bag without their knowledge, or by paying it back through stratagem? And is one absolved of the responsibility by doing so?

The debtor's obligation is not discharged except by paying his debt to its owner or his representative. The payment can be actual, such as handing it to him, or constructive, such as placing it in his box and informing him of that, as the creditor might discard it if he does not know it is his debt.