I would be a bit skeptical of using straw in a greenhouse as it makes a good hiding place for bugs. I would pile it a unused corner of your property or mix it into the garden soil somewhere.

I would just till it or fork it into the soil.

i don't take the straw off my garlic, I let it grow right through it.

Why don't you want to use it for mulch?

Let the garlic grow through it until a couple weeks before harvest then rake off. This is common practice. Garlic cannot handle weeds. Using straw in the garden is terrific! Still, that said, if you don't want to except for garlic (I am weeping about that) you could use it on garlic again if there is no disease present. Garlic has little pests. The upper Midwest had a severe garlic disease last year so it does get diseased!

And here I was thinking of taking it off so that sun would warm the ground, since I didn't even plant the garlic until February, and I figured it needed to get rolling in order to have a chance to produce a crop this year. Based on the input above, I'll just let it ride for now.

Thanks, everyone.