Oh, I love that you want to help your grandmother. 🙂
If you have the whole picture of her drawing (it looks like it gets cut off on the right side), you can open it in Photoshop. Then you can remove the writing and drawings inside the larger letters a few different ways. Here are a couple of simple ways:
Option 1 - Select inside each letter and fill it with white:
Use the Rectangular Marquee Tool (you can use the Search in Photoshop, the Magnifier in the upper right, or click in the Tools. It's the 2nd one down. If the Elliptical Marquee Tool has been selected, you can click and hold to access the Rectangular Marquee Tool below it.)
Draw a selection inside a letter
Fill the selection with white (If you click on the tiny black box and white box near the bottom of the Tools, Photoshop will set the foreground color to black and background color to white) by going to Edit > Fill and in the Fill dialog, select Background Color and click OK.
Repeat steps 2-3 for the other letters
Option 2 - Use the Eraser Tool to erase the contents of each letter:
Select the Eraser Tool (It should be the 12th tool down, or you can press "E" to access it)
Make sure the size and hardness of the Eraser are set for your image (You can check in the Options bar at the top. If you don't see the Options bar, set the Workspace the icon in the upper right, directly to the right of the Photoshop Search and set it to Essentials). The Brush Settings for the Eraser will be two icons to the right of the Home icon. Click on the dropdown to the right of the shape and number to set the size, hardness, and shape (if necessary).
Move your cursor around where you want to erase the markings inside each letter
Hab es jetzt geschafft die Buchstaben zu füllen jedoch ist da eine farbliche Differenz zum äußeren Ausschnitt. Wenn ich diesen mit dem Füll-Werkzeug füllen will, verschwinden die schwarzen Linien. Kann mir jemand helfen?
You could do the same process of either selecting or erasing outside the letters to make it the same color.
Another way to make the selection that you could try is to select the Quick Selection Tool (It's 2 below the Rectangular Marquee and looks like a brush with a dotted circle). Draw with the Quick Selection Tool on the areas outside of the letters. You can hold down Shift to add to the selection. Then fill it with white.