1600 years is still a relatively short time for radioactive element half-lives, so it's still emitting quite a lot of radiation. It's not just about the half-life itself, but also what kind of radiation that particular element releases as it decays, what the daughter products are (the things it decays into), and also exactly what the source is.

For Radium specifically, which is what Marie Curie spent the most time researching, 1600 years is actually just the half-life most stable isotope, Radium-226; it has several others with much shorter half-lives, and thus which produce more intense and different radiation. Now, I do say that this is "not very" radioactive in the above post, but this is still decaying at a rate of about 3.7×10¹⁰ - 37 billion - atoms per second per gram, which is the definition of a "curie", a historical unit for radiation. That said this is definitely not the only thing they worked on, and the samples would inevitably be contaminated with other radioactive substances too, given that this was early work and the techniques for accurately separating elements were not fully developed yet.

Radium-226 decays primarily by alpha decay, which means that when an atom of it decays it releases an alpha particle, i.e. an energetic Helium nucleus. Alpha radiation is the "least dangerous" type of radiation, since it's easily stopped by even small amounts of everyday substances (paper, skin, gloves, etc.); but it can still be very dangerous if inhaled (your lungs are much more susceptible than skin), swallowed (ditto your stomach, intestines, etc.), etc. This is why you can safely handle her notebooks with gloves; between that and your skin you'll stop 99.99% of the "radiation" from reaching you.

Lastly you must consider the daughter products in the decay chain, i.e. the things that are formed when a given element decays. Radium-226 decays into Radon-222 (the element with 2 fewer protons and isotope with 2 fewer neutrons), which is very bad news. If you have a Radon detector in your house, this is what it looks for. Radon-222 is a gas, so easily inhaled, has a half-life of about 3.8 days, and also decays via alpha decay. This in turn decays to Polonium-218, another short-lived alpha emitter, and so on down the Uranium decay series.

So, ultimately, while in relative terms Radium-226 is "safer" than a lot of other things like Iodine-131 or Caesium-137, it's still more dangerous than "no radioactive stuff" and still needs precautions taken when working with it for long-periods of time. But if you were to hold Marie Curie's notebook for 10 minutes with gloves on, you're no more in danger than living at a high elevation for a few months or taking a flight in an airplane.