I think it is made of ABS (acrylonitrile butadiene styrene). It's definitely not fibreglass.
I have a turbo one for sale if you are interested.

If you can get the cover made for it, covering the hole completely will reduce airflow through the engine bay. When I mentioned what I was going to do to the mechanic they said they'd do it when they put in the new alternator. They used a spare piece of plastic they had laying around and charged me $10 extra so its definitely cheap and easy!

Screw the battery, go capacitors! Save weight with style and innovation

The turbo lid doesn't have a steel frame. It is completely plastic though does have metal rain shields

Yaaayyyy.
 
Just got confirmation that the alternator definitely being replaced under warranty by an Auto Electrician instead of the mechanic.  They will also rig up a cover when they put the new one in, checking battery as well.  And fixing electrics in driver side door that have been playing games for a while.   I will have to pay something for the door part of it, but once I had her towed to the Auto Electrician I didn't have to talk to the Mechanic any more.  Gibbo's Auto Electrics took it from there.
They will have the new alternator tomorrow & the plan is to have her ready to go by tomorrow afternoon.

Interesting to read.
 
Just in case there's other people out there looking to purchase a new alternator for the Toyota MR2 MK1, please be aware that there is a shonky chinese job on the market that proclaims to suite the car, but doesn't.  I know as it smoked in approximately 8 months in my own vehicle and upon taking the vehicle to another autoelectrician I learnt that the incorrect type had been installed in the first place(although the first autoelectrician I took the vehicle to swears black and blue that there manual states it can be used).  The funny thing was I had all kinds of electrical troubles and they kept saying things like: 'the age of the vehicle' and 'something else is probably wearing out' etc etc. 
 
With the replacement 'CORRECT' alternator, I have had ZERO electrical problems and everything runs perfectly, so don't listen to B/S.  Looked after, the Toyota MR2 MK1, is a superb reliable car.  (It also helps to have mechanics and autoelectricians who know what there doing and who you can actually trust).

I picked my baby up yesterday afternoon. 
They fixed the wiring in the drivers door as well, but the tweeter cover fell off half way home.  They said to call in & they'll sort that out.
I also decided to check what the cover over the alternator looked like this morning.  When I shone the torch down there I could actually see the wiring inside the alternator .  Waiting for them to call me back to tell me why they didn't make the cover they said they would.  Feeling a bit nervous in the rain, so I have covered the engine cover.  Altho the original alternator lasted almost 24 years without a cover, so it should be ok.