Does the body really gets rid of all gadolinium from an mri? will having a slightly non alcoholic fatty liver affect the process?

Yes & No: If you have normal kidney function, 98% of the gadolinium dose is excreted in your urine and out of your body by 24 hours. The rest is eliminated in your stool. A mild fatty liver shouldn't affect this.

No and likely yes: In absolute terms, it is highly unlikely that every single molecule of gadolinium-based contrast is eliminated from the body. Despite the fact that gadolinium can be deposited in the liver, at this time, liver disease is not regarded as a concern for administration of gadolinium-based contrast agents.