Staying safe involves some compromises. Walking her dog through the garden isn't going to put your grandmother in immediate danger, but digging in the garden and emptying the cat's litter box are best avoided.
Being around other people is a matter of degree. She shouldn't be afraid to be out and about in general, but she shouldn't spend lots of time in a crowd of strangers or with people who have colds. If she swims, she should be careful not to swallow the water. I'd avoid it if I had any exposed cuts.
See
What Precautions Do I Need to Take After an Organ Transplant? and
Care at Home for the Immunocompromised Patient for some typical safety tips. The first of these sites tends toward the lenient side. The second of these sites is rather strict. That's because opinions differ on how much you should curtail your activities in the name of safety, versus quality of life. It comes down to an individual's decisions.
Remembering that it's temporary makes it a lot easier to cope with safety restrictions. When treatment is complete and immunosuppression is in the past, the rules can be relaxed.
My wife avoided restaurants and many types of raw fruits and vegetables while she was the most immunosuppressed. Later she eased up on the limitations, but still avoided buffet-type eating, such as salad bars, and skipped having sushi, which she really likes. Finally, she felt safe enough for normal restaurant and eating habits, but to this day she's a bit more safety-conscious about food than the average person.