That's butyl putty. You can buy it in a tape roll. It's pretty cheap. It's used for moldings like that, windows, access hatches, stuff like that. It dries out on the edges after a time, but underneath it's probably still soft and pliable. I personally would not remove the molding, just trim off the putty and caulk it.
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Chuck
2013 Jayco Jayfeather X20 E (sold)
2016 Chevy Silverado LTZ 2 Z71 Crew Cab (sold, and dearly missed)
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