This is one of the cases where the one-size-fits-all rule does not work. There are several possible renderings available and being used, such as “pull effect”, “call effect” (you dislike it), “magnet effect”, etc. Just judging by the simple number of hits on English pages, “pull effect” seems to be the winner, and that is the reason why I am posting it as an option in this query. But this does not mean at all that other feasible options are worse or even wrong.

As for the “inspiration”, I do not know, really. I think “pull effect” works well, but, again, I am sure there are other good alternatives.

https://www.files.ethz.ch/isn/31901/WP 30, 2006.pdf
Spain’s Immigration Experience: Lessons to be Learned from Looking at the Statistics
XXXXX
Working Paper (WP) 30/2006
1/12/2006

However, the most spectacular finding is not the significant drop in the number of irregular immigrants in Spain, but some information in the INE’s press release, when it made public the results of its analysis of the local population register. According to the INE, the net increase in the number of foreigners enrolled in the local population register was 650,000 in 2004, compared with 647,000 in 2005.13 A net increase of 650,000 immigrants is indeed an intriguing piece of information since it contradicts the popular notion that the extraordinary regularisation campaign should have triggered a ‘pull effect’ (efecto llamada) in 2005 bringing more new immigrants to Spain than in a normal year.

https://www.migrantsrights.org.uk/downloads/policy_reports/i...
IrregularMigrants:
The urgent need for a new approach

The Spanish regularisation had the backing of employers (some believe it was employer driven), trade unions, NGOs and the Spanish regions. It has been criticised from a number of perspectives – some critics were concerned about the level of migration and the long term impact particularly when the economic situation deteriorates; regions were unhappy that the financial benefits largely go to the central government rather than the regions; some worried about the likely pull effect. The exercise itself was described as daunting and stressful, but has been cited with approval by many policymakers

https://www.bbc.com/news/world-europe-19487321
Spain's migrant healthcare dilemma
By XXXXX BBC News, Madrid

However she also says Spain's free public health system has contributed to a "pull effect", making it "very attractive for immigrants, especially illegal ones, to come to Spain".
The new law will, she argues, make it "more difficult" for those people and may reduce the "pull effect" now and beyond Spain's financial crisis.