Biological data being used by an unpublished research paper is considered proprietary
The copyright is probably on the full database release flatfile and the formatted entries ... you will find similar conditions for UniProt/SwissProt so it is not so unusual.

The restrictions on scripts are common to prevent server performance hits from a large number of requests.

You can simply invite reviewers to download the data from some other server, for example from the EBI SRS server. The URL for entry A00673 would be

"http://srs.ebi.ac.uk/srsbin/cgi-bin/wgetz?[IMGTLIGM-ID:a00673]+-view+FastaSeqs+-ascii" 

You can also use a list of accessions, for example A00673 or A01650

"http://srs.ebi.ac.uk/srsbin/cgi-bin/wgetz?[IMGTLIGM-ID:a00673|a01650]+-view+FastaSeqs+-ascii" 

If downloading many entries you should pause between requests, but putting lists into the URLs may reduce it to few enough not to cause a problem. I doubts EBI would be upset by 200 requests - they would be concerned about thousands.

There are various fasta formats available for IMGT data, you need to find a server that produces fasta files compatible with your input requirements.

Alternatively of course your reviewers could download the whole database from IMGT or any of the other servers (including ftp://ftp.ebi.ac.uk/pub/databases/imgt/) and generate their own fasta subset from the list of accessions/ids

Hope that helps!