As you stated steganography hide data in less important piece of information of a source (because the goal is hide data within other data affecting them less as possible).
In no way pure steganography protect the message hidden, it's only a tool for hiding.
Image you would hide message "AB" in a grey scaled bitmap 4x4 (0-255 value per pixel).
Eg :
Convert message in bit :
"AB" > hex -> 65 66 -> 01000001 01000010
Do the same thingh with your image (0 is black 255 is white, grey between) :
____
|####| 0 0 0 0 00000000 00000000 00000000 00000000
| # |--> 255 0 255 255 --> 11111111 00000000 11111111 11111111
| # | 255 0 255 255 11111111 00000000 11111111 11111111
|__#_| 255 255 0 255 11111111 11111111 00000000 11111111
Foreach bit of your messaage, sobstitute the less significant bit of the
corresponding byte of the picture so :
Message Original Picture Resulting Picture
0 00000000 00000000
1 00000000 00000001
0 00000000 00000000
0 00000000 00000000
0 11111111 11111110
0 00000000 00000000
0 11111111 11111110
1 11111111 11111111
0 11111111 11111110
1 00000000 00000001
0 11111111 11111110
0 11111111 11111110
0 11111111 11111110
0 11111111 11111110
1 00000000 00000001
0 11111111 11111110
Original Picture | Picture with Message
00000000 00000000 00000000 00000000 | 00000000 00000001 00000000 00000000
11111111 00000000 11111111 11111111 | 11111110 00000000 11111110 11111111
11111111 00000000 11111111 11111111 | 11111110 00000001 11111110 11111110
11111111 11111111 00000000 11111111 | 11111110 11111110 00000001 11111110
As you can see message stored in that way (in the bitmap) does not have a great impact on the way on which human percept the image (pixels are pretty equals before and after).
The algorithm i have described is very naive but the principle is the same in every steganography algorithm.
In your case there is not bitmap but JPEG (a complicated way to represent image, complicated because there are compression algorithm), and there is a password and encription.
Encription is there for two reason, secure the message (steganograpy alone does not guarantee any confidentiality) and create a noise like distribution on less significative bits (normally less significant bits has such distribution but an hidden message may deviate that distribution in the Resulting Picture, so an attacker can identify which pictures hide a message).
If you wuold be sure that an image does not hide secret data you don't have to try to find them.
Mainly beacuse every steganograpy algorithm is particular and store information in a different way (the only limit is the immagination), secondly because if steganograpy is done properly (with robust encription) you can not distinguish between noise and hidden data.
So the only approach that seems to me pratical is try to manipulate the candidate picture (a picture that could contain hidden data but also could be a regular picuture) in a way that a side channel will be broken.
In my naive implementation a manipulation for cleanup could be a compression with JPEG, JPEG is pretty close to bitmap (to human eye), but the less significant bit will be whipped out (due to compression) and hidden information with them.
In your specific case i suppose that taking the picture and compress it again with JPEG (using a greater factor of compression) should also work.
Remember that every steganography algorithm is particular so one may store hidden data in a redundant way, tryin to be more resilent to your cleanup endeavour (see watermark tecnique : Digital Watermark).