There are a few misconceptions in that question.
Inventory shares held by market makers are owned by them. Jn order to become a maker in the market of an OTC company stock the OTC requires the brokerage to hold a precentage (?) of the OS of that company as inventory. To guaranteed number of shares within buy/sell quotes placed on the electronic trade system.
Trading liquity is very thin in many OTC companies and the 2 tier OTC market was set up to solve that problem. It's the job of M&Ms to close orders from inventory when matching trades are not available.
Next I do not recall a tender offer being a reason to hault a stocks trading.
Next tender offers are normally at a premium to share price. The offer price does not determine any new stock price.
Next I can't recall ever seeing a tender offer to buy shareholders shares for an OTC company. This is seen on big board companies. When a deep pockets individual or money management firm wants to gain some control of a company they feel has made poor management decisions. Like an Carl Icahn deal to get a seat on the board of directors.
Now for the question;
When a tender offer, to buy shareholders shares, is made public, retail will often buy with the big guy. This causes the price to increase. The retail reaction , not the offer price. The offer is made to major shareholders, within the company. Ones which own over 5% of the stock. It's not normally a public thing, but the public is who raises the stock price. The 5% owners tender their stock if excepted. (no matter the stock price @ the offer price) The offerer gets increased voting power for a premium price. Two different buckets of stock (insider and public).
Yes if retail increases the price the OTC "market makers" inventory value increases, just like any shareholders stock and gains are realized.
But Remember; tender offers, unlike mergers or public share offerings, are made mainly to accumulcate outstanding shares, to increase company ownership through the back door. Used as a tool to gain voting rights, while removing possible opponents to a new company direction at the same time. And will increase the individual or groups existing power within the companies decison making structure. You don't see this often on the OTC. And market makers are on the OTC.
The big boards use specialist to open and close orders, but they do not hold an inventory. They just seek the best price for their client base.