What is the recommended number of mounting count for IBM LTO 7 tape.

I'll echo Nicolais comments - further, the life of a tape is probably most determined by how they are treated and handled / stored.

A previous firm I worked at had tape libraries located in a different location than the clients (so backup were automatically off-site).  We never took the tapes out so they were kept in a perfect environment (correct humidity / temperature) and not jolted around by being moved.  We had thousands of 'active' tapes, and rarely had a failure, just the occasional one.  Way way more reliable than disk ....

Some years ago I was talking with Imation, their technical guys who did a lot of the development and testing work.  They agreed that the no mounts was not a good way to determine tape life, in fact it was pretty meaningless.

No. of end-to-end passes was better, but still not that good.

There used to be a product called Storsentry, it was written by the guys that developed, or were involved in development of DLT tapes, I forget the company name.  This interfaced with the backup product, and monitored tapes and drives for low level errors that would normally not be seen, and could predict tape/ drive failure before it happened, it was amazingly accurate.

Many companies would just replace their tapes every 3 years 'to be safe' - following analysis of environments with Storsenty a high percentage of tapes had no issues - I forget the numbers but it was something like 95%.

LTO life is not measured by mount counts. The lifespan is measured in passes from the head, and it depends on how many tracks the tape has (different numbers for different LTO versions).

LTO7 is capable of performing 1000000 or more passes.Copied from https://www.lto.org/active-archiving/
LTO tapes have an archival life of more than 30 years. They can support a million passes and 20,000 write cycles per tape, and they have a mean time between failure (MTBF) rating of 250,000 hours at a 100% duty cycle. Data integrity technology is built in with block-level checksums.

LTO7 has 3584 tracks. copied from https://images-na.ssl-images-amazon.com/images/I/913ApiTq6UL.pdf

As a result, if a tape is mounted and completely written in each mount, the minimum number of mounts is 279.
In real life, this number will be higher as a tape loads and unloads several times before getting full.
In the environments I administer, I have LTO tapes that have 3 or 4 thousand mounts.

check also
https://tapeonline.com/lto-7-faq

I would recommend to add rule in inventory robot with max mount of 1500 is safe bet