Update after speaking with my wife:
As usual, Rex is almost completely wrong about everything (laugh).
Kumi’s translation is spot on: it’s a parent speaking to their own kid, saying not to overtake the boss’s kid. It’s NOT two adults speaking to each other prior to the event.
This “overtake” connotation for 抜く is not one I’d ever encountered before.
That is, 抜く here is not like the common expression
昼飯を抜く • skip lunch
but expressly like
先頭走者を抜く • overtake the lead runner
(Both examples from the Kyudansha JE dictionary. I sure wish I’d read past the first example in the dictionary to see the latter!).
So riffing on @Kumirei’s translation, the most “poetic” translation I can come up with is
Sports day: Don’t overtake — that’s the section chief’s boss.
In hindsight, the 抜くな wording is uncomfortably direct/rude/speaking-down. It’s something a parent would say to a child, but not how you’d normally speak to a peer.
Apparently I was completely wrong about any ambiguity. I thought the writer was wondering about which reason the day was circled (garbage or birthday). She said that to her the poem is unambiguously a sorta sad/chagrined but laughing realization that the day is circled because its garbage day, not because it’s the writer’s birthday.
So despite my arguments about the grammatical point, highlighting that the writer’s birthday is circled it would confuse the meaning if you wrote it that way in English.
So the simplest translation without introducing anything extra that still captures the sense might be:
Garbage day circled, my birthday