Everyone’s talking about filling dame here, but OP was asking about etiquette of defending a cut:
I’m almost certain the marked stone is dead and white’s territory is safe. But with plenty of points to spare, I might reinforce it just in case or to head off pointless invasions. Either way I can’t imagine anyone getting annoyed by one or two extra reinforcement stones that are costing you points.
When my opponent reinforces something I thought was secure, it makes me wonder whether I missed a good opportunity to attack. Here’s a similar position I encountered recently where I didn’t miss it and Black really should have reinforced earlier:
(Or was it actually safe? I don’t know.)
And apparently even the pros fail to reinforce critical points sometimes: