PBEWithMD5AndDES Cipher does not check for integrity first?
Password-based encryption uses a hash function to derive a key from a password and that is the only use of a hash function. PBEWithMD5AndDES itself doesn't provide any authentication (includes integrity) and only uses MD5 for key derivation.

If you want authentication, then you can still use PBEWithMD5AndDES, but you then would have to derive a MAC key from the password yourself and generate an authentication tag by running HMAC(ciphertext, macKey).

But it is not recommended to use DES or even MD5 nowadays, so you should change the encryption scheme nevertheless. If you do, then you can exchange it with AES-GCM which already provides authentication. You still would need to derive a key from a password that you provide. There are many key-derivation functions, but Java provides PBKDF2 in the standard library. Alternatives are scrypt, bcrypt and Argon2.