The free option that's getting the most attention right now is definitely Adobe's Generative Fill feature in Photoshop, though you need to check if it's available in your subscription tier. It's genuinely impressive at inpainting - basically you select the object you want gone, and the AI fills in the background. Results are usually pretty natural looking because it's trained on massive datasets. If you're not into Photoshop, Google's Magic Eraser (built into Google Photos and Pixel phones) works surprisingly well for casual photobomb removal, and it's completely free if you use Google Photos.
For a standalone desktop app, Cleanup.pictures is browser-based and free to start with, though they have paid tiers. The output quality is decent for most scenarios. There's also Inpaint from getinpaint.app which gives you more control - you can paint over what you want removed and adjust settings like brush size. Windows users sometimes swear by TouchRetouch but that's not free. The real variable is how busy your background is. If there's a lot of detail or texture behind the photobomber, even the best tools might struggle and you'll see some artifacts or blurring. Simple backgrounds like sky or ocean? These tools handle it really well, maybe 85-90% of the time you get something that looks totally natural.
My suggestion is start with Magic Eraser if you're on Android or have Google Photos, since there's zero friction and it's free. If that doesn't cut it, try Cleanup.pictures - the preview is instant so you can see if it'll work before committing to anything. The key is having realistic expectations; these tools are magical for some situations but they're not perfect wizards yet.