Maybe.

Time travel introduces all kinds of bizarre elements which don't necessarily interact well with one another. If your only constraint here is that one individual replace their own grandmother in a single instance, and that reality itself will bend to accommodate that while maintaining continuity, it is perhaps not literally impossible for this to happen through natural-esque mechanisms.

But the overarching issue is that, if people are free to travel into the past and do whatever they want but cannot change outcomes, then you've fully defined the system. It's that assertion that describes what's possible, not real mechanisms interacting with a fantasy mechanism with immutable properties. Because you've already fully specified the outcome, and that outcome has no particular basis in reality, then the word possible doesn't operate here in the same way it does in everyday English.

Some problems:

A view which begins with a metric of genes-in-common is too simplistic to describe this situation. Key events in human reproduction include mutations, crossing over, and environmental factors, including epigenetic factors, all of which exist independently of genes-in-common. Further, it's trivially possible to have the same proportion of genes in common while not actually having the same, specific genes in common, and for continuity you really would need the latter.

Let's define A as the "original" grandmother, B as the mother (who is to be borne to her own time-travelling daughter), and C as the time traveler. These introduce several (million) points of failure into the scheme beyond simple availability of specific genes.

In the broadest case, which you've considered, it's entirely possible that C will lack genetic information which B inherited from A, and therefore C cannot pass them to B. That situation would mean that B cannot be generated from C.

The other issues I mentioned include an extreme degree of randomness-- the same chromosomes being replicated by the same process under the same circumstances may see alleles reorganized in new ways-- it's the same gene, more or less, but it may not work in quite the same way as the original did.

Mutations also matter, in a similar broader way. The molecules which make up DNA may be altered by a variety of factors, literally changing the blueprint which defines the organism. A similar issue is introduced by epigenetic factors-- environmental effects which influence which genes are expressed, and how often.

There are many, many other factors which would matter here (this is a poor summary of a miniscule subset of relevant information). But the underlying mechanisms you're hoping to rely on are far more complex than what was presented in the question, and so a solution that delves into that level of detail would automatically require more detail in order to be even naively valid.

The solutions

Of course, time travel itself is a totally undefined activity in real-world terms, and so you can introduce any properties or constraints that you want onto it. This would be enough to overcome any conceivable problem with the scheme, as the "rules" of time travel can simply override them by fiat.

Most of the first-order problems with this sort of loop are a result of randomness: which genes are available, and which specific events occur during cellular reproduction and organism development. If time travel inherently enforces continuity, you can hand-wave all of that away. C simply would have the correct genetic information, present in the correct configurations, in the correct structures, at the correct times to replace A silently.

In short, because you've already asserted that the outcomes of events which have "already" occurred cannot be changed, then all possible problems simply fix themselves or are conveniently elided. You don't need any mechanism to do this, because it's all time magic in the first place.

I would posit that the bigger problem is that, because A gave birth to B, there is no way to change events such that C would give birth to B. If time is fully deterministic, as indicated in the question, then it's questionable (at best) for that change to take place-- what would A be doing instead of being pregnant and delivering B?