Suzanne, if they ae checking out the box then they've pretty much made your decision for you. I would let them become attached to the box, even allow them to start building a nest and then trap them. You could take the passive approach and just remove nests as they build, but it could take weeks for them to finally give up, if they do, and your box would be unavailable for native birds during this time.
I have used the Gilbertson trap with great success on all my trails.
Kathy

Here is a link that might be useful: Gilbertson in-box trap

The HOSP has already bonded to the box and won't give it up. I have both Gilbertson and VanErt traps and both work well.

If you think that allowing the HOSP to nest peacefully to keep them busy will work, you must think again. At the first sound and sight of HOSP, be ready to eliminate them.

Linda

Congratulations on the Dee's. U R so lucky to have them nest with u. I keep hoping every year they will choose 1 of my nest boxes.
I agree with the others...get rid of the hosp. If ur chickadees come back next year and so do the hosp...u will have MAJOR problems. Take care of the problem now.

Karen

I have pretty much made up my mind to get rid of them but I don't know how to do it kindly. I put duct tape over the hole while I was waiting for input here and it's been ripped off! Don't they fly off if they hear you approach the box? How would I trap them in there? Then what?

You need to get an inbox trap. I use the VanErt. Your questions are good ones. Like you, I had never had HOSP until I put up boxes for the native birds. This spring I had to trap my first HOSP and I had many of the same questions as you. This forum helped me a ton. I don't remember who answered me, but she said to let the HOSP bond with the box for a few days, then set the trap at night and he would go in it first thing in the morning. That is exactly what happened. I was also told to tape a leaf over the orange dot on the trap, so he wouldn't be suspicious of it. I did that and also glued some grass over the trip wire. As for the "Then what?", try looking at the sialis website for the most humane way to euthanize him. The first time is really hard. But I knew if I didn't do it, I would soon have nothing but HOSP. I wish you the best of luck.

I use the VanErt trap as well. It is very important that u monitor the trap and 2 make sure u have not trapped a native bird. Go 2 www.sialis.org for all the information u will need.

It's not a HOSP but a house wren! Are they as evil as the HOSP? I moved the box today and because it's closer I can see it clearly.

Yes, House Wrens are pretty bad. However, they are protected by federal law, so you cannot trap them. You can, however, keep removing the sticks they put in there. If you're not trying to attract more Blues, I would just take that box down or plug it up.