This was a popular accessory back in the 50's and 60's. The curb feeler would give an audible warning when approaching a curb. It was particularly useful for preventing "whitewall rash" on those easily scuffed whitewall tires. Curb feeler design ranged from purely utilitarian to more somewhat whimsical. Sometimes installed as singles on the cheap, often installed as a pair on the passenger side of the car, occasionally installed as a pair on both sides just to be cute.
Wide stripe whitewall tire and curb feelers on an MGA, photo from Gary Edwards in Kernersville, North Carolina, USA