1. Select Layer → Transparency → Add Alpha Channel
2. Select the background using the Fuzzy Selection Tool (Magic Wand) and press the Del key.

GIF will allow you single-color transparency, while PNG has full alpha channel support.
See also GIMP Watermark removal

1. Select a path with the Fuzzy Select Tool
2. Select menu Select → To Path
3. Select the Flip Tool
4. Select Affect: Path and Flip Type: Vertical
5. Click into the layer with the selection to flip the path
6. Select the Text Tool and type the text
7. Right click into the text box and select Text along Path
8. Select menu Layer → New Layer
9. Select Path to Selection in window Paths - Brushes / Open the paths dialog
10. Select the Pencil Tool and paint the text
11. Select menu Layer → Transform → Arbitrary Rotation, set the center point, and rotate the text
12. Right click on the temporary layer Floating Selection in window Layers - Brushes and select To new Layer
13. Delete any layers not needed anymore

This is for text along a circle in the bottom of the circle. For the text on top of the circle, omit steps 3-5.

• Text along Path
• Text Along Path - GIMP 2.8 Tutorial For Beginners

1. Right-click on the layer, select Layers –> Add Alpha Channel
2. Right-click on the layer, select Layers –> Duplicate Layer (not necessary, just to be save to have a backup)
3. Make copy visible only, then Select All, then select the Fuzzy Select Tool and click into the background area
4. Select Selection to path, and again Path to selection, and make the path visible
5. Right-click on the layer, select Add Layer Mask…, choose Selection and click Add
6. Go to Image –> Fit Canvas to Selection, and save

• How to Erase and Replace Any Image Background in GIMP 2.10
• GIMP 2.10 Basics: Using the Foreground Select Tool

Resynthesizer allows you to remove watermarks and similar from an image. Download it from the GIMP Plugin Registry or my wiki. Move all files to GIMPPortable\Data\.gimp\plug-ins\.

For an example, see GIMP Watermark removal