As long as it's in a bottle under 100mL, it's no problem*, though I've never had any issue with it in the US either. I've been refilling the same 100mL Clear Care bottle from my full-size bottle for quite some time now.

A quick search indicates that some people got it confiscated when it set off ETD machines, but I've never had that experience, and I travel quite a bit in Europe now and used to travel a lot in the US.

*edit in response to mod comment: it's no problem in Europe; I've been through security in most of the countries of Western Europe and the only time it's ever gotten a second look was when a security staffer at MAN gave it a quick glance to see the "100mL" marking on the bottle.