I think this book review by Nelson Goering of Robert Mailhammer & Theo Vennemann's book "The Carthaginian North: Semitic Influence on Early Germanic: A Linguistic and Cultural Study" at https://hcommons.org/deposits/download/hc:40752/CONTENT/goer... and https://doi.org/10.1075/jhl.20028.goe does a good job of summarizing the argument and the review author's issues with it.
> The thesis presented in this book – that there was a substantial linguistic impact on what would become Proto-Germanic from the Punic spoken by Carthaginians who allegedly established outposts in northern Europe – has been argued by one of the authors in various articles for many years (see the collected articles in Vennemann 2003, 2013), and is already known as ‘controversial’. ... This book can be taken as arguing the best possible case for Punic influence on Germanic ...
> This, then, is the sum of the strictly linguistic evidence marshalled by MV for the alleged Punic contact and linguistic influence on Germanic. They supplement it with an appeal to writing systems, arguing that runes are best derived directly from the Punic alphabet. They make a number of points, but a large core of their argument turns on the supposed derivation of the first four runes (for f, u, þ, and a), in order, shape, and sound, from the Punic alphabet. .
> The result of this, it should by now be clear, is that I must conclude that the central thesis of the book – that there was linguistic influence from Punic on pre-Germanic – is not supported by the evidence marshalled here. More than that, I would say that this Punic hypothesis may now be confidently rejected as very probably untrue. If such influence were real, then the combined labours of two talented linguists, one working on the problem for very many years, and with ample (if often critical) feedback to build on, would have uncovered convincing traces by now. That they have not strongly suggests that such do not exist. If this is the best argument that can be made for the Punic hypothesis, then the hypothesis would appear to be incorrect.