Probably hidden in the carpet pile.try using a small screwdriver and use it to feel around until you find metal . Or a magnet to search.
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It was a rainy few days at Algonquin Prov park...tarps kept us dry.
Wayne --Belle River (Windsor), Ontario
2013 Sunset Trail Reserve 25RB..(just sold it)
2015 White Chev Silverado 2500HD 4x4 (6.0 l gasser)
2003 Mountain Star 890SBRX Truck Camper
My bet is there is not any screws, but about 3 dozen very thin staples that are barely long enough. May want to inspect it from the backside from the basement, mine had no support on the back edge of the step, just sort of hanging waiting for someone to fall through, I cut blocks for support & no more squeaking.
If looking from the top, you'll most likely have to peel the carpet back to add screws.
We carefully removed the carpeting and replaced the plywood step with a prefinished oak tread from Home Depot.
I wanted to screw and Gorilla Glue it in place BUT the DW saw a storage opportunity.
MODIFICATIONs were involved and after a few hours the new step with cleats on it's bottom rests into the opening without wobbling.