Intermittent "no route to host" in combination with "unmeshed response with l5d-proxy-connection set"

[ngc4579]

We are running a StatefulSet workload meshed with Linkerd (2.12.3, control plane already upgraded to 2.12.4) and are intermittently experiencing issues like these:

{"timestamp":"[339989.694070s]","level":"INFO","fields":{"message":"Received unmeshed response with l5d-proxy-connection set"},"target":"linkerd_app_outbound::http::proxy_connection_close","spans":[{"name":"outbound"},{"addr":"<redacted>:7653","name":"proxy"}],"threadId":"ThreadId(1)"}

{"timestamp":"[339989.694023s]","level":"INFO","fields":{"message":"Request failed","error":"error trying to connect: No route to host (os error 113)"},"target":"linkerd_app_core::errors::respond","spans":[{"name":"outbound"},{"addr":"<redacted>:7653","name":"proxy"},{"client.addr":"10.96.21.136:50576","name":"rescue"}],"threadId":"ThreadId(1)"}

{"timestamp":"[339989.686792s]","level":"INFO","fields":{"message":"Received unmeshed response with l5d-proxy-connection set"},"target":"linkerd_app_outbound::http::proxy_connection_close","spans":[{"name":"outbound"},{"addr":"<redacted>:7653","name":"proxy"}],"threadId":"ThreadId(1)"}

{"timestamp":"[339989.686737s]","level":"INFO","fields":{"message":"Request failed","error":"error trying to connect: No route to host (os error 113)"},"target":"linkerd_app_core::errors::respond","spans":[{"name":"outbound"},{"addr":"<redacted>:7653","name":"proxy"},{"client.addr":"10.96.21.136:37416","name":"rescue"}],"threadId":"ThreadId(1)"}

{"timestamp":"[339989.684433s]","level":"INFO","fields":{"message":"Received unmeshed response with l5d-proxy-connection set"},"target":"linkerd_app_outbound::http::proxy_connection_close","spans":[{"name":"outbound"},{"addr":"<redacted>:7653","name":"proxy"}],"threadId":"ThreadId(1)"}

{"timestamp":"[339989.684270s]","level":"INFO","fields":{"message":"Request failed","error":"error trying to connect: No route to host (os error 113)"},"target":"linkerd_app_core::errors::respond","spans":[{"name":"outbound"},{"addr":"<redacted>:7653","name":"proxy"},{"client.addr":"10.96.21.136:59516","name":"rescue"}],"threadId":"ThreadId(1)"}

The <redacted> target IP points to a service outside of the cluster (C# based service hosted in an IIS) - its logs show no access whatsoever in the respective time frame.

Any hints on how to track the core issue further down? Does Linkerd provide additional diagnostics that might shed some light on this?

Does a no route to host actually indicate network issues with connections leaving the cluster towards an external system? What does Received unmeshed response with l5d-proxy-connection set mean in this context?