It’s not even about NiMH vs Li-ion, which is better, although @darylm is correct that Li-ion is better in many ways and hence has become more popular. It’s actually about what the ConnectClip is designed to use, and as a result, what the charger inside the ConnectClip is designed to charge, because a charger for Li-ion cannot be used to charge NiMH batteries, and vice-versa. You don’t want to be charging a NiMH battery using a Li-ion charger or vice versa because it’s not safe nor is it proper to do so in the first place.
I have a specially designed charger that is microprocessor based and is designed to charge both types of battery chemistry, either NiCad/NiMH or Li-ion, by using a different charging algorithm/process for each of the chemistry type. But that’s a box the size of my palm that can charge up to 4 batteries of different types independently. The tiny little charging circuit inside the ConnectClip can’t afford to be that smart, so it’s most likely dedicated to charging Li-ion batteries only.
Besides, not only NiMH and Li-ion are different type chemistries, they also have different voltages across a single cell. NiMH is 1.2 V, and Li-ion cell is 3.6 V. OK, you can stack 3 NiMH cells in series to get the 3.6 V of the Li-ion, but again, there’s no room inside the ConnectClip to place that many NiMH cells to replace the tiny little Li-ion cell anyway.