It is best to clean out the basket and remove ALL bags, parent trays, hoods, cupholders, toy bars, etc. from your stroller *before you leave home*, and pack those parts in your checked luggage. This is especially true if they just snap on and off. (If they come off with a screwdriver but stick out away from the stroller frame, you might as well pack the screwdriver in the checked luggage and do it properly. If they are tightly screwed on and fit flush to the frame of the folded stroller, you can probably leave them on without too much risk.) Remember that the main hold inside the aircraft is not usually pressurized; it gets VERY cold in the hold, which tends to make the plastic components on a stroller very brittle and more apt to snap, especially if it is hot on the runway, which creates a really broad temperature change in just a few minutes.