The Creator made three pure metals to be magnetic at room temperature. One is iron, which we all know, the second is nickel (older Canadian coins are very high Ni, and are magnetic. The current production is lower in Ni, and non-magnetic at room temperature). The third alloy is cobalt.
If one starts with pure nickel, and progressively alloys it with more and more chromium, it goes from being magnetic at room temperature, to being non-magnetic.
The same is true of cobalt. Common high temperature alloys based on cobalt, e.g. Haynes 188 & 556, L-605, have sufficient Cr in them to be non-magnetic at room temperature.
The most common reason for a piece of Inconel alloy 600 (UNS N06600, nominal 76%Ni 15.5%Cr bal Fe) to be magnetic is, as has been said, that it has been carburized. Carburization forms chromium carbides, removing Cr from the matrix. Once enough Cr is occupied being a carbide, the Ni matrix becomes low enough in Cr to be magnetic at room temperature.
Hot corrosion from various alkali metal salts also can make Inconel 600 magnetic. In this case the Cr selectively oxidizes and not only becomes a chromium oxide, or alkali metal chromate, it may be physically removed from the chunk of metal in question.
The same thing happens to the common heat resistant alloy RA330 (UNS N08830), mominal 35%Ni 19%Cr 1.2%Si 1.5%Mn balance iron. It has long been practice amongst heat treaters to check their alloy fixturing with a pocket magnet. If the metal is strongly magnetic, it cannot be weld repaired, for one reason or another. Carburization makes the metal too brittle to weld without base metal cracking. Hot salt corrosion physically penetrates the metal with salt & makes weld repair both unpleasant and ineffective. If magnetic, just sell the fixture as scrap & buy a new one.
I never did catch why you cared that your 600 alloy was magnetic, or what it had been used for?