Anemone Dillema

[Delphinus]

I agree, the anemone can usually fend for itself. If it can't sustain itself without opening into the area, it will likely move. As long as it has a place to move to that suits its needs. I did have a BTA move into the back of my rockwork once, it went into an area of low flow/definitely-low light, and emerged on the other side about a week later, about half size and somewhat bleached out. With that said, it did recover and regain its zooxathellae and size within a few weeks after that. As long as it can still occasionally feed (and is eating the proper foods) they can be very hardy.

I think it's pretty normal for the fish to keep the eggs area clear.