διεκδίκηση basically means claim in such a context, but since ‘the restaurant under claim’ is unsuitable in this text, we should look for a likely synonym of ‘claim’, which we could use instead. One of the meanings of ‘claim’ is ‘to request formally’, but you don’t have to use the word ‘formally’ when using the word ‘request’, because it would be understood in a context such as this one that the request is being made formally.

Another alternative would be “the restaurant being sought”.

For examples for “the requested restaurant”, see:

The Franchise Agreements executed in accordance with this Agreement for ... in compliance with the Development Schedule, or if the requested restaurant(s) ...
http://www.sec.gov/Archives/edgar/containers/fix180/1289728/...

Oct 16, 2012 - G) Consideration of a Motion to award a contract to Aqua-Aerobic ...... case, convenience stores, as well as the requested restaurant, are not ...
http://www.statesboroga.gov/wp-content/uploads/formidable/10...

44.11.07 – Request to consider a contract for a lease agreement for a .... to the issuance of the requested restaurant retail liquor license contingent on the Fire ...
https://www.homewoodal.net/print.php?id=August 27, 2007

May 22, 2014 - The omission of the requested restaurant may have reflected shortcomings in Apple's database of local businesses. Beyond that, Siri performed ...
http://economictimes.indiatimes.com/tech/hardware/apples-car...

For examples for ‘the restaurant being sought’, see:

May 1, 2008 - ... into which the user can insert the name or a portion of the name of the restaurant being sought. Once those two simple selections are made,
http://www.google.com/patents/US20080104059

A location plan of the premises is shown at Appendix B. 3.4 The licensable activities and operating times of the premises being sought are as follows: ...
http://apps.n-somerset.gov.uk/cairo/docs/doc21367.htm

Nov 18, 2010 - He said he couldn't elaborate on the circumstances surrounding the decision to move, or on the premises being sought. Hudson Madison ...


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Note added at 1 hr (2015-06-25 16:52:02 GMT)
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Sorry, the internet reference for the last item under “the restaurant being sought” is:

http://www.albertalocalnews.com/business/Hudson_Madison_relo...


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Note added at 1 hr (2015-06-25 16:58:29 GMT)
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Of course, as an alternative form of wording to the first option, you could say. “the restaurant being requested”.