So I bought a used Remington 700 in 338 lapua magnum.

When I extract rounds, if I work the bolt slowly they fall out just as they should. But when I work the bolt quickly the rounds stay on the bolt face, failing to eject. I'm thinking I need to upgrade the extractor. But it doesn't appear to be a factory deal, it looks like someone upgraded it, the bolt looks like it's been milled out for a different one.
Since I bought it used, anybody know what I need to do to upgrade this bad boy?
Thanks in advance.
-Steve

If the case is coming out of the chamber, its extracting. What its not doing right from what you posted is ejecting. I would remove the firing pin assembly and clean the bolt body with a good solvent and blow it out real good w/ compressed air, and put some red shooter's choice grease (the kind in the syringe) into the ejector- not a ton of it, just a blob about the size of a bb) then get an expended case, hook it into the extractor at the rim, and work the rim back and forth on the ejector compressing the spring and trying to work that grease into it, then wipe the excess red grease off of the bolt face w/ a q tip, replace the firing pin assembly into the bolt, lightly lube, and replace the bolt in the rifle.

Sako sells a replacement ejector, it's hella spendy but it comes with a free rifle.

The 700 Remington seems to have issues with extraction and ejection with cases larger than the standard 30-06 (2.5"), Wild West Guns in Anchorage, Alaska does a package on 700s which adds the Sako type extractor and adds a second ejector (looks like your halfway there ). I had a 338 Ultra Mag done several years back and it worked well.

More than likely the ejector edges need to be rounded, it is digging in to the brass locking it up between the ejector/extractor tension. See that silver crescent on the face of the ejector in your second photo?

That caught my eye immediately... but I have nothing to offer...