"Adaptation" is generally used in the sense of adapting premises for special use whereas "settling in " is what someone does in the early period of a new job. I think the Hebrew suggests the latter rather than the former.

According to the link below, מענק הסתגלות is defined as:
מענק הסתגלות - פיצוי בעד ימי מחלה שלא נוצלו
http://www.hargal.co.il/Info.aspx?txtParam=CT_ADV&txtItemID=...

Which is easy enough to grasp, but finding an English equivalent is not so easy. I found one link:
Unused Leave at Retirement
Sick Leave
At retirement, you may receive service credit for up to 90 days of unused sick leave from your last employer at no cost to you. This service credit cannot be used to establish retirement eligibility. Sick leave is reported by your employer after retirement. One month of service is granted for each 20 days of sick leave.
http://www.retirement.sc.gov/scrs/active/basicinfo/default.h...

This "service credit" as they call it seems to match the description of מענק הסתגלות quite well - a type of compensation for unused sick days - redeemable upon retirement.

It seems that some companies include this payment/grant as an adjustment to the retiree's retirement package (hence the הסתגלות I guess).

In the "target term" I have included two terms that I came across (links included below) that sound like the מענק הסתגלות described in my first link.

It might be a complete tangent(hence the low confidence), or you might not end up using either term, but hopefully it might point you in the right direction.

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Note added at 18 hrs (2011-11-19 17:30:26 GMT)
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Sorry - you're right, in the course of my research the grant did seem to be a "catch-all" type thing, for anyone who leaves employment for almost any reason (retirement, another job, fired etc).

I've given this another shot as a separate answer because my previous answer was getting long.

This seems to be more of a catch all term (for severance, retirees, redundancies etc).

It also has an incentive element to it (i.e. if you leave the company two weeks early it can be counted as your accrued leave
Or.... alternatively if you work until your notice date you will receive a full accrued leave payout etc....

This may be grasping at straws, but I thought it was worth another shot.

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Note added at 20 hrs (2011-11-19 19:53:30 GMT)
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No problem, I think I'd do the same. Adjustment Grant is the best option available. I obsess over these things, especially the ones where you ALMOST find the right answer, and then you keep telling yourself if you keep researching for a bit longer you'll magically stumble upon the perfect answer - it's more frustrating than the questions where you know for sure you'll never find an answer and accept giving up more easily. Anyway, I'm rambling, enjoy the rest of your weekend!