In addition to Demetri's answer (+1):

1. The use of GAM is well-established in the field of Ecology so I would add certain books/influential articles. Show you are not reinventing the wheel rather that you are abreast with modern modelling approaches.
2. You do not describe your sample size but you might want to try a validation schema to show that through the use of GAMs you get better goodness-of-fit. While hand-wavy if something like an AIC/BIC shows a clear preference for a particular model this can pacify some (not too sophisticated) criticism...
3. I would emphasise how the GAM fitting procedure looks into shrinkage. It is plausible that someone oversimplified GAMs in his/her head as "a polynomial basis of sorts" and therefore prone to overfit.
4. Take their view-point for a moment: are there any established studies suggesting logarithmic, or exponential decay curves already? The reviewer might be satisfied that you acknowledge them as a possibility. Maybe you can make a critical assessment of that prior work and show how your work is a step forward.
5. As Dimitri mentioned, specifying a functional form without prior knowledge can induce strong bias. You can politely double-down on the fact you are using a non-parametric approach. Maybe even try a different basis functions (e.g. cubic regression splines and thin-plate splines) and show how the results are (hopefully) very similar and thus not dependant on the choice of basis functions.

Just to be clear: In my opinion, using GAMs is the correct approach here; the criticism of "why not X-functional form" is weak. Such criticism might be warranted if prior research suggested robust evidence for a particular modelling assumption but even then it would not be a particularly strong position to take.

In addition to Demetri's answer (+1):

1. The use of GAM is well-established in the field of Ecology so I would add certain books/influential articles. Show you are not reinventing the wheel rather that you are abreast with modern modelling approaches.
2. You do not describe your sample size but you might want to try a validation schema to show that through the use of GAMs you get better goodness-of-fit. While hand-wavy if something like an AIC/BIC shows a clear preference for a particular model this can pacify some (not too sophisticated) criticism...
3. I would emphasise how the GAM fitting procedure looks into shrinkage. It is plausible that someone oversimplified GAMs in his/her head as "a polynomial basis of sorts" and therefore prone to overfit.
4. Take their view-point for a moment: are there any established studies suggesting logarithmic, or exponential decay curves already? The reviewer might be satisfied that you acknowledge them as a possibility. Maybe you can make a critical assessment of that prior work and show how your work is a step forward.
5. As Dimitri mentioned, specifying a functional form without prior knowledge can induce strong bias. You can politely double-down on the fact you are using a non-parametric approach. Maybe even try a different basis functions (e.g. cubic regression splines and thin-plate splines) and show how the results are (hopefully) very similar and thus not dependant on the choice of basis functions.

Just to be clear: In my opinion, using GAMs is the correct approach here; the criticism of "why not X-functional form" is weak. Such criticism might be warranted if prior research suggested robust evidence for a particular modelling assumption but even then it would not be a particularly strong position to take. That said, try to see where they are come from too, criticism can be helpful strength your manuscript and/or alleviate worries of future readers too.