Understanding network performance impact of 32 bytes per request

My company is using redis on a fairly performance critical path. An nginx server calls out to it once per request. The call itself has several arguments, which are currently like 80 bytes. This call goes over the network to redis, which passes the args to a lua script it has loaded and then makes a decision and returns it.

My boss thinks that adding an additional 32 byte string to those arguments is unacceptably bad compared to hardcoding the string in the lua script (which sucks for other reasons), because "if we get 50k requests in a second, that's 1.6GB of additional network traffic in that second." My intuition is that this is not a concern. The traffic is from an EC2 instance to an ElastiCache instance, and I think that because of how packets work, and how small the request already is, those 32 extra bytes are very unlikely to incur significant processing cost in the network stack at either end. Am i totally wrong?