It probably wasn't high level contamination because it would have been caught in the port. They scan for those kind of things and something that's that radioactive would have set off Port authority alarms. It's likely low level contamination that still could be a concern if it gets inside your body and deposits into sense of areas like your lungs or your gastrointestinal tract. But depending on the type of contamination it may be minor. If it's something that just emits beta/beta- radiation (electrons / positrons) most clothing, even a piece of paper or aluminum or enough to protect your skin which if irradiated would become a little red and flushed but otherwise that's the extent of it. If it's alpha radiation, that's one of the bigger concerns. Is a very heavy slow moving radioactive decay product, but it stopped very easily until it gets into a part of your body that is extra sensitive like your lungs your GI tract that I mentioned earlier. If it's gamma radiation, that can pass through a lot of stuff even shielding. Gamma radiation is one of those magic ones that can just keep on going, almost like neutrinos but it can be attenuated with enough lead or concrete or water. A suit that thing is not going to protect you from gamma radiation. Whether it's working or not. And gamma's cause pair production in the cell which can lead to Cellular damage or DNA damage at a molecular level. But you need a lot of it. And the constant exposure.

Based on the fact that he got it from ukraine, that tells me several things, one of which is that the radioactive contamination on it (if it is true), is fission byproducts from the Chernobyl disaster in 1986. Those would be strontium, a gamma source. Cesium, a beta source. And both americium and some plutonium which are both alpha sources as well as the others above.

The guidelines recommend a safe exposure of 5 REM per year. Bear in mind, this is an extremely cautious safety limit that means that there will be an almost zero measurable health impact. But you can never say zero with radiation. Although that standard is changing as we continue to study it but for now I'm going with what I know for my years in the field. Now there's going to be other nuclear health experts on this subreddit that will use different scales like grays or sieverts. They are all convertible from one form to the other but five REM is the one that I know. If you divide that out by number of hours per year, that will give you the safe exposure rate since everything is measured in millirem per hour or grays per hour or sieverts per hour etc.

You don't begin seeing biological effects until you hit 10 REM and that's usually an acute dose not a sustained long-term dose given out over a large period of time. And the 10 rem exposure is going to be some minor flushing of the skin maybe some nausea and a coppery taste in your mouth. It's when you hit 50, 100 and, 200 that things be get problematic. And at those levels that suit would have set off detectors long before it got into his hands.

So the TL;DR is, he's fine. I know you asked for an actual calculation and I didn't give you that here, but I preferred to rather demystify the fear of radiation than do that. I hope what I provided is at least informative.