Composting grass damaged by grass grub

Does anyone know if it is safe to put the grass that was torn up by the birds, (they are eating grass grubs underneath) in the compost ? I have a nasty feeling that I might just be incubating dear little new grass grubs. The lawn looks horrible, bald patches with a few new bits of torn up grass. I have just mown it to try and clear up a bit of the mess, and am debating whether to put the contents of the catcher in my compost. I raked it a couple of times and put the dead grass in my red bin. I have bought a VERY expensive product to sprinkle on the grass to kill the grubs, but it doesn't seem to be working, called LawnPro by Kiwicare. They swore it would kill grass grubs, I had trouble sprinkling it on as it has a top with little holes to help sprinkle but it didn't come out easily at all. I felt like levering that bit off but the warnings about how poisonous it is were so dire I didn't do it. Help please !
it is called Lawnguard

The grass grubs live in the soil and eat the roots of the grass which is why it is easy to pull out, it should be fine in your compost the worms will deal to it and turn it into lovely compost for your garden,
https://www.google.co.nz/?gws_rd=ssl#q=Grass+grub+life+cycle
This may help to understand the little nasties.

http://www.kiwicare.co.nz/help/problem/?sid=grass-grub http://www.kiwicare.co.nz/help/problem/?sid=porina

It sounds highly probable that your problem might actually be porina as opposed to grass grub. Your best bet would be to dig a spit (spades width and depth) and actually identify what you have. If you do have grass grub then you have really missed the boat to treat the grub at this stage of the year. Lawnguard prills are highly effective if used correctly and at the correct time of year.

I've heard that a good frost kills them.

thank you everyone, I am pretty sure it is grass grub, little white curls of grubs.
although I think it is a bit late I have put the Lawnguard stuff on the lawn, and now we have had a REALLY good frost, 4C (Christchurch) so I probably needn't have bothered. I will attack it again in spring.