Small ring of water sitting around tub

[Isaac H]

So I am in the process of installing my claw foot tub. I have installed the drain and it is not leaking. However, because of the nature of it being an old tub, there is a small ring of water around the tub drain. This is purely because of the deep slope of the drain area and the lack of a depression in the tub like modern tubs have. Is there anything I can do about this or is this small amount a non issue. Will water always pooling like this eventually cause issues with the plumbers putty and seep through or something?

 

[Isaac H]

Interestingly, when I run water the water pretty much completely drains. But when the water is filled in the tub I actually just noticed that the standing water is actually on top of the drain flange, and there is some water surface tension that is keeping the water from flowing over the edge. Hard to see in this picture, but it's similar to when a glass is filled over full the but the water stays in the glass because of surface tension.