If the stubborn strainer is made of any magnetic metal, you can try poking a telescoping stick magnet tool down the drain. Hopefully it will stick to it and pull it out if it's not stuck. Otherwise, you'll have to remove the trap or some of the plumbing underneath to get it out.
Thank you for your inquiry. Yes, this would fall into a 1.25 inch drain. Unfortunately, we do not offer a basket for that size drain.
The Danco 80058 Strainer measures 1-1/4 inch across the TOP LIP and fits perfectly into the plastic 1-1/4 tailpieces currently supplied with most bath faucets. Unfortunately, this item's "specifications" do not make this measurement clear. Even the blister pack CARD says: "1-1/16" OD x 3/4 DEEP", confusing the issue. This is a GREAT PRODUCT and will most likely work perfectly for your 1-1/4 bath sink drain application. DANCO - Please take note and add the TOP LIP 1-1/4 dimension
Thank you for your interest in Danco products. The Danco 1-1/16 in. Sink Basket Strainer in Chrome, model # 80058, has a depth of 3/4".
Thank you for contacting Danco. At this time, we do not have a sink basket strainer that is smaller than 1-1/16 inches.