I would keep the runners unless you have more than enough within your area. If that's the case, let them root and then transplant them.

Marla

X 2 what Marla said

Take the runners off. I have been growing the ever bearing for about 12 years now. You also want to take the dead leaves off and any spent berry falls (or falls with just 1 or 2 small berries). I find pulling off the falls encourages the plants to start back into flowing more quickly than not plus too many on the plants makes it hard to harvest come fall.

Seasscapes are everbearing/day neutral strawberries and you always remove the runners from such. I am growing seascape for the first time and have been getting berries from the plant for about 10 days and they are some of the best I have ever had.

I also grow Albion ever bearing which are not as good tasting but one of the prettiest berries I have ever seen