I'd just let it be in the deli cup it came in then, if you have space to fit a water dish and leave a little toom for the spider. They don't need tons of room to themselves, especially obts because they like to hide a lot anyways. The other things are molts, yes. You could leave them there or take them out, whatever tickles your fancy.
Once the spider molts with you then you will probably have to rehouse it because it'll probably outgrow the deli cup. By then it may have settled in more and be a bit chiller (don't expect miracles lol but maybe just a bit!) And therefore easier to move. Good luck!
P.S. if you're really determined to get it out of the deli cup now, choose a day when you have time to work with it, leave the deli cup open in the critter carrier and bother the crap out of it with a chopstick (with the lid mostly on the carrier, open just enough to fit the chopstick in) until it comes out of hiding, then nudge it along away from the deli cup until it's far enough away that you can remove it.
Or you could try putting the deli cup on an angle right in front of the cork bark so it can see that there is somewhere to hide and it may then decide to go hide under the cork bark after.