Thanks Dizzle Problems - I believe from the graphics and funky grips it is a 1986 model. Like our other Giant built Schwinns a lot so this should be fun to get back on the road!
The foam was only good for protecting the chrome. I just take a knife and slice them off. The old grips can come off the same way unless you want to save them.
Maybe those grips are worth saving. One way to slide them off is to get an open ended wrench that will just fit over the handlebars on the the inside of the grip, then take a mallet or hammer and tap the wrench to pop it off. I've used an adjustable wrench also.
Very nice find! Those grips look to be cooked on. Doubt you can remove them without cutting them off. The foam grips above are really nice and I have put them on a couple of my bikes. Very comfortable!