I did grade 1 jazz flute last session - did the St James Infirmary Blues, Moonglow and Everything That Lives Laments.
I think that when the head returns, particularly if it's a repeat of what's been done before, then you're on safer ground embellishing, as you've proved that you can play what's written!
It's bee a while since I played the pieces, but things I can remember doing:
St James - may have transposed part of the return of the head up an octave, definitely added extra notes/grace notes, and played around with the rhythm - I think I also added my own little flourish at the end which was marked as a rest. Got 27
Moonglow - I know I changed a few of the notes and added a couple of grace notes/runs. I think I may have played with some of the rhythms a fair bit in the repeat. Got 28.
Everything That - I think I may have played with the head just a little even before the solo... small runs between notes/grace notes, but not a lot... in the return, I changed it loads, changed bits of melody, bits of rhythm, added runs, grace notes, played in a different octave. Got 29.
I think that if the embellishment leads to any doubt that you can actually play what's written then you're on dangerous ground, but if it's a repeat of something you've already played as written and/or if it's clear from your playing that you have a total command of the music and you're just going mad (& it fits in well with the music) then you're OK.
In the flute books it says that on the first playing "notation should be closely followed. While there may be variation in details of melody, rhythm or phrasing, the result should be coherent, stylish and musical". They also point out that it's likely to vary depending on the particular piece.
In the "after the solo" section, it says "everything here may be embellished in any number of ways, from a few simple additions or variations to a more extensive reworking". The guidelines they suggest are;
grade 1 - small changes in rhythm or melody, variation in dynamics or phrasing
grade 3 - transposition at the octave, fills
grade 5 - more intricate melodic lines, rhythms and phrasing reinterpreted.
They also suggest that "exact repetition of earlier material should be avoided".
Just to comment on what Sue has said:
QUOTE
On the whole, perhaps good to encourage your student to explore as much as possible, in the interests of becoming a better jazz player?
AMEN!
If your student experiments and keeps trying out new things, it will help him develop more as a player, and both you and he will get a feel for how much is "too much" and when it sounds like he really just has a feel for things. IMO (and not a terribly experienced O but anyway

) ideally one should go into a jazz exam (or any jazz improv experience) not knowing entirely what one will play in the solo or during the head... by all means get the chord patterns into your head and try out loads of different things, but be ready to just go with the flow and have fun come the day of the exam! It may be a bit risky in the exam room but I think at least that it's better preparation for actually playing jazz

ps hope this post makes sense, I got a bit overexcited and waffled a lot...