Is there a way to minimize the black stipes before varnishing?

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There are always "ways"...... to do any type of cover up of unwanted wood characteristics. The question is how much time do you want or have to spend doing them??
If that time expenditure is not already built into this project, or any other projects you contract to do, then it's up to you whether or not you can personally absorb the monetary losses involved or not, along with an explanation to your customer
Of whatvyou r going to do and a sample of what the end results will look like.!!
On the other hand, if this is a personal project and you don't mind spending lots of time tanning out the dark areas, and all other steps you will need to do and still end up with a less than perfect results as to the areas not being totally invisible, then I can be of help.

Chemmy,
Time is not a problem. I was thinking to use bleach. Would it work?

We are doing a huge bookcase in teak. Designer wanted teak but now wants it a blond color. We have at least 10 samples from 1-3 coats of two part bleach to using thinner to take the oil out. Now he likes a sample we used stain on to lighten to wood. Paid 6 grand for the veneer and he could have saved a lot by using a lighter wood. We used a bit of titanium white UTC for the color. FYI.

Hey dr, well you got one reply that shows you a way forward, it will work, to varying degrees, A lot of times teak bleached out quite well.
But I have to ask if you liked the color of the teak to begin with, at least to the degree that you spent your hard earned money on it to begin with, why would you now want to bleach the color out? So I will suggest what we, did when existing already built or manufactured furnishings owned by purchasers, who for whatever reasons, like the wood color but not the mineral streaks or dark areas, such as seen in sparked woods etc. We would do this.
In most cases the techniques were called bleach toning for lighter to medium colored woods, or others called it tanning be cause they used a tan color as the base, like on cherry or mahoganies etc,. your free to call it whatever you like.!
Just keep in mind that these are all pigmented coatings, or stains/ glazes, etc. dyes are not used in these first steps.!
1) step will be to match the color of the surrounding teak as close as possible, but if anything just a little lighter.
2) with an artist brush or a fine tipped airbrush, apply the color to only the dark areas you want to lighten, if air brushing, do not use a coating to mix the color into, the color must be one that can be manipulated with brushes, rags squeegee's etc. If you want the best results. You in turn can mix a thin air brushable coating and go over those same areas multiple times, with good sucess, but if your goal is to cover just the dark areas and nothing else, only a glaze that is manipulable, can accomplish that.!
3) Once the color is applied and has been worked out to your satisfaction, and left to dry, it can be sealed in and again be evaluated as to its acceptable or unacceptabllity.! Do not judge the color while the clear coat is freshly sprayed, most likely it will appear lighter than after the coating has dried for hours or over night.! If the next morning it looks acceptable to you, then a few further steps can be taken to disguise it even futher, like hand applied grain color matching, maybe some small variances of color being artist brush applied, etc. Whatever it takes to blend these areas in to disguise their darkness, even thin coatings of thinned out dyes can give back some color clarity that a natural wood has, if done deftly.! Also if absolutely necessary, you can apply a ghost coat, ( an extremely thin application of the same color over the whole panel) to also blend it in., those are decisions you will have to make on your own.!
4) Then finish out as you would if not having taken these steps.!
Hope this helps, if not disregard and follow someone else's advice.
Chemmy

PS: as always " DO THIS ON SAMPLES FIRST" never on the actual project.!!!

Chemmy,
You are more complicated than my mother-in-law. Good advice but very time consuming. This two 4x8 sheets I am using are 25 years old, paid like 60 bucks each, yesterday they quoted me one 1/2" sheet at $390, almost fell off my chair. The best and cheapest way would be to just buy a paper backed veneer sheet and glue on top but I already have 3 coats of varnish. I will leave the settee (marine dining area) as is and hope to like it when it is finished. Thanks everybody.

Sorry, you stated that " time was not a problem" ....hope whatever u do works out to your satisfaction.!
Reguards...chemmy