First, it is important to know that the designated reply-to of a sent email (through SendGrid or otherwise) will be the email address used for human replies. Second and according to email RFC (see part 4.), the return-path address of a sent message will be responsible for receiving automated "out of office" or other messages.
Automated replies to the return-path and human replies to the reply-to are simply the standard protocol. The recipient inbox should have the ability to customize how their replies (automated or human) should be routed to either the reply-to or the return-path. This is the preferred path forward as to how the recipient inbox reads these options should be within their control.