The Java code you link to uses ECB mode to encrypt the data, which is extremely insecure (look at this Wikipedia article for a simple and graphic explanation of why). To be frank, taken together with the well-known weaknesses TEA has, you probably might as well not bother encrypting your data at all if you use this method.

If you absolutely want to use TEA in EBC mode you can't use Crypt::Tea, since it sensibly uses CBC mode (as you've already found out). You'll have to implement it yourself, the algorithm basically consists of a few lines of C, so this shouldn't be too hard ;-). I'd recommend going the other way though and modifying your Java code to use CBC as well (not rocket science either).