Regarding a question about something that already happened, we should consider the matter from two perspectives: What is best to do in similar future circumstances? If what was done was less than optimal, can we legitimize it after the fact?
The first question is whether Birkat HaGomel applies to a katan (minor), even one who is old enough to perform mitzvot. The Maharam Mintz[2] says that it is inappropriate for a katan to recite the beracha because of the beracha’s language. We[3] say “… hagomel l’chayavim tovot (Who does favors for those who deserve punishment).” In other words, the one who makes the beracha acknowledges that had the danger been actualized, it would have been deserved because of his sins. However, a child is not culpable for his sins, and it is improper for the child to suggest that it is his father who is culpable.[4] The Maharam Mintz does not deem it an option to alter the beracha’s form and leave out the issue of culpability.[5]
Despite the existence of dissenting opinions,[6] the consensus among poskim is to not require a child who is saved to make a beracha[7] and even to discourage it.[8] Furthermore, you seem to be speaking about a child who is too young to be obligated or able to make the beracha himself. In such a case, the poskim do not obligate anyone, including his father,[9] in his stead.
It is important to note that Birkat HaGomel is modeled after the korban toda (sacrifice of thanksgiving).[10] Beyond specific halachic requirements, there are various ways to show thanks to HaShem. These include making a seudat hoda’a (meal of thanksgiving) and giving tzedaka, which are appropriate in the case you describe. On the other hand, some may feel a lack of fulfillment or may fear a bad omen if no one recites HaGomel. It is not always wise to argue with people who feel this way. Thus, let us see if a voluntary beracha is possible.
The gemara[11] relates that when Rav Yehuda recovered from an illness, disciples who visited him noted their gratitude to HaShem for saving him for them without using the HaGomel formula. Rav Yehuda remarked that he was thereby exempted from reciting HaGomel, and the gemara explains that it was because he had answered “amen.” The Rosh[12] explains that the students, who felt personal joy at their rebbe’s recovery, were not required but were permitted to make the beracha. The Beit Yosef [13] rules that with the exception of disciples regarding their rebbe, one should not make the beracha about others.[14] However, Ashkenazim should note that the Rama[15] says that anyone who feels the happiness may make the beracha. The Mishna Berura[16] assumes that this is true even if the one who was saved is not present (which similarly applies if he is too young to understand). Thus, while one should not make a practice of saying berachot for others, we can justify the grandfather’s beracha in the case you describe.
As we saw above, we are hesitant to change the beracha’s text, and it is therefore unclear whether one who recites HaGomel for someone else should omit “l’chayavim” to avoid implicating others.[17] He should change the text (composed in the first person) and indicate who was saved. This is not considered changing the beracha’s form but rather applying it to the correct person.[18]
However, there is some logic in keeping the word “l’chayavim.” The Taz[19] suggests that only one who feels the joy of the other’s salvation may make HaGomel for him. We thus consider it as if he is thanking HaShem on his own behalf for saving someone close to him. Therefore, he says, the mention of culpability might refer to the one reciting the beracha. In the same vein, use of the first person in describing the favor bestowed can also be justified.
In conclusion, while not recommending the course of action taken by the grandfather, we need not reject it either.