How does a business decide when not to make a recommendation?
Write down the reason for a recommendation before you create it. Tie it to a current customer task or an expressed preference, and ask what useful decision it enables. A detail that predicts a possible interest doesn't earn an interruption.
The anticipatory-experiences discussion included the idea that a brand may create value by using less of the information available to it. That makes a handy design exercise.
Timing matters. A relevant suggestion can still land badly when it's repeated, arrives after the task is done or competes with more important information.
Let people dismiss it and adjust the preference behind it. If a recommendation rests on an inference, make correction possible, and don't treat that inference as a permanent fact about the person.
When you test, include people who choose no recommendation at all. See whether they understood why it appeared and whether declining was easy.
Measure what the interruption costs along with the response. Your team may find that one useful suggestion serves the customer better than a string of increasingly specific messages. I'd keep that as a result to test.
What to try this week
Take one recommendation your business already sends and write the reason it exists in one sentence, naming the customer task or preference it connects to.