Make up some rules
It’s not remotely scientifically realistic. Why would that keep you from using it? Just declare that gravity on your world works like EM radiation and is transmitted by graviton particles. Most materials interact with gravitons by expressing a force of attraction, but attrahite does something else.
Here is one scenario consider. Lets say that gravitons are like neutrons. Neutrons will penetrate many objects to a decent distance, and even when they do not pass through without a collision, they are scattered. But some specific elements (Boron, Halfnium) absorb those neutrons instead. Attrahite could absorb gravitons in a certain way, completely removing gravitic energy and transferring it to some sort of atomic energy, much like the energy of neutrons absorbed is partially transfered to strong force bonds in the new nucleus.
Another thing to consider if you go with the above model, is that some energy that is absorbed can be re-released by certain processes. Certain energy gamma rays can be abosrbed in a crystal lattice. If that lattice is heated, the energy is re-released. This is the principle by which thermoluminescent dosimiters work. Atttrahite could absorb gravitons, then be induced to release them by heating, exposure to sunlight, chemical reaction, or something.
There are of course infinite other scenarios dending on what you determine the gravitons to act like. Are they like electrons in that they have a 'gravitic charge' that attracts or repels them, and attrahite is the only other compound with a 'gravitic charge'? Is attrahite the only material that interacts with gravitons by repulsion? There are so many options.