The gun on offer from Vintage Firearms is a model 334, just as Jay describes. It is not a "Grade 4". No such thing. There had been prior to 1931, but this gun was made in the immediate aftermath of WWII, my guess from the serial number by 1950. And in 1947, when production started up again after the war, they started on the second model designation since the "Grade 4" term had been used.
What it does have is 4 laurel barrels. (Sometimes called "wreaths"). The general barrel quality and proof loads are given a shorthand designation with the stamp of laurels, typically between 1 and 5 laurels. In theory they go up to 7 laurels but I've never seen anything higher than 5. The 4 laurels this gun has means it's pretty good. Wall thickness is about where I would expect. Most Ideals in NA do have wood damage, often from smiths who don't know how to disassemble them and who break the wood in the process.