I guess it depends on which species. Are they all are within a single taxon? If so, doing a search using ´higher_taxon` might be the easiest way, e.g., all accepted species names in Lepidoptera:
Web:
https://www.gbif.org/species/search?rank=SPECIES&dataset_key=de8934f4-a136-481c-a87a-b0b202b80a31&highertaxon_key=159955155&origin=SOURCE&status=ACCEPTED&advanced=1
API:
https://api.gbif.org/v1/species/search?rank=SPECIES&dataset_key=de8934f4-a136-481c-a87a-b0b202b80a31&highertaxon_key=159955155&origin=SOURCE&status=ACCEPTED&advanced=1
In the results, you not only get the taxonKey (field key) but also the matching species in the backbone (nubKey)
If your species of interest are not in a single group, you can also search for them individually by sourceID, e.g.,
https://api.gbif.org/v1/species?datasetkey=de8934f4-a136-481c-a87a-b0b202b80a31&origin=SOURCE&advanced=1&sourceId=urn:lsid:dyntaxa.se:Taxon:214018
In the latter case, a simple script would probably come in handy to retrieve all 3000 species.
If I’m missing your point completely, do let me know 