The toy keyed checksum teaches the check-before-accept concept only.
Changed bytes would need a different tag
Recomputing over key plus changed message gives tag 0xce22, not the old tag 0xd622.
0xd622=0xce22
Check before accepting
The concept is simple: authenticated bytes are checked before the receiver accepts the message.
check first=1
What this does not model
NOTE: toy keyed checksum only; not HMAC, not AEAD, not nonce handling, not side-channel safe, and not production authentication.
production MAC=0
Summary
A real design uses real authentication, but this toy shows why the changed bytes cannot keep the old tag.
old tag valid for changed message=0