User Matthew is correct that a nipple extractor may help you salvage the tee.
You need to check the threads in the Tee for any damage, since if the threads are scratched you may get a leak.
If the tee is badly damaged
If the tee can’t be reused, you will need to replace it. This part is readily available at any home-improvement store (but see below).
It’s good that you can remove the pipe clamps if needed, but the Tee fits into the end of the hose with a very tight pressed fit. You may need a “vise-grip” style clamping wrench to get a good enough grip on the fitting.
You may have to cut the black polyethylene hose to get the tee out. In this case you may even need a straight coupler to repair the black hose.
Here is a cheap one for less than a dollar:
This is a relatively fancy one, but even this only costs $1.28:
A word to the wise
Based on personal experience, I have found that big box home improvement stores sell a grade of sprinkler PVC fittings that is not the same as what the professionals use.
For example, the replacement nipple sold at a big box store will cost about 69¢ and be made of a very lightweight grade of poly propylene (PP).
The types of tee, also, used by professionals are much heavier weight and durable. It’s well worth buying a $1.50 tee from a professional plumbing or professional landscaping supply house, rather than the $1.00 tee sold at the big “orange and blue” stores.
When you consider your time, and the damage from having to tear up your grass and dig the hole again when the cheap part inevitably breaks again, it’s no contest.
If you don’t know a local sprinkler store, you can mail order from specialty stores online. You’ll be glad you did.
Don’t use a nipple
These days, a professional sprinkler company/irrigation contractor would not use a “nipple” to replace this fitting, even though you currently have them in the ground in your system.
As you can imagine, any exposed sprinkler head that can get stepped on, run over by a lawnmower, or run over by a car tire if it is next to the driveway, can cause the head to break the nipple off.
Beware this piece of junk: it costs only 59¢ but when it breaks next year, it will cost you another afternoon of your time to replace it.
The correct replacement is to use a flexible riser pipe, or “swing joint”, known in the trade as a “funny pipe.”. Funny pipe is flexible and will protect the fitting from future damage so you don’t have to replace it again.
Any new installation of sprinklers should typically use funny pipe.